%! /TeXDict 200 dict def TeXDict begin /Mtrx matrix def /@start { /StartTime usertime def vmstatus pop /@VMused exch def pop 72 720 translate } def /@letter { /letter where { pop letter 72 720 translate } if } def /@legal { /legal where { pop legal 72 936 translate } if } def /@note { /note where { pop note 72 720 translate } if } def /@a4 { /a4 where { pop a4 72 765 translate } if } def /@landscape { [ 0 1 -1 0 0 0 ] concat -648 0 translate } def /@manualfeed { /manualfeed where { /manualfeed true put } if } def /@duplex { /setduplexmode where { /setduplexmode true put } if } def /@copies { /#copies exch def } def /@startdoc { dup 72 exch div dup neg scale 0 0 transform round exch round exch itransform translate Mtrx currentmatrix pop currentdict /isoddpage known { /SecondMtrx matrix def 8.5 exch mul 0 translate SecondMtrx currentmatrix pop }{ pop } ifelse /@TeXSave save def } def /@restore /restore load def /restore { vmstatus pop dup @VMused lt {pop @VMused} if exch pop exch @restore /@VMused exch def } bind def /@pri { ( ) print ( ) cvs print }def /@newfont { /newname exch def newname 7 dict def newname load begin /FontType 3 def dup neg matrix scale /FontMatrix exch def /FontBBox [0 0 1 1] def /BitMaps 256 array def /BuildChar {CharBuilder} def /Encoding 256 array def 0 1 255 {Encoding exch /.undef put} for end newname newname load definefont pop } bind def /ch-image {ch-data 0 get} bind def /ch-width {ch-data 1 get} bind def /ch-height {ch-data 2 get} bind def /ch-xoff {ch-data 3 get} bind def /ch-yoff {ch-data 4 get} bind def /ch-tfmw {ch-data 5 get} bind def /CharBuilder { exch /BitMaps get exch get /ch-data exch def ch-data null ne { ch-tfmw 0 ch-xoff neg ch-yoff neg ch-width ch-xoff sub ch-height ch-yoff sub setcachedevice ch-width ch-height true [1 0 0 1 ch-xoff ch-yoff] {ch-image} imagemask } if } bind def /@dc{ /ch-code exch def dup 0 get length 2 lt { pop [ <00> 1 1 0 0 8.00 ] } if /ch-data exch def currentfont /BitMaps get ch-code ch-data put currentfont /Encoding get ch-code dup ( ) cvs cvn put } bind def /@pc { pop /ch-data exch def currentpoint translate ch-width ch-height true [1 0 0 -1 ch-xoff ch-yoff ] {ch-image} imagemask } bind def /@sf { setfont } def /@flushfonts { @TeXSave restore /@TeXSave save def} def /@bop0 { pop } bind def /@bop1 { pop Mtrx setmatrix /SaveImage save def } def /@eop { showpage SaveImage restore } def /p { moveto } bind def /r { 0 rmoveto } bind def /s { show pop } bind def /ks { 2 1 counttomark 2 sub { -1 roll } for counttomark 2 idiv { show 0 rmoveto } repeat show pop } bind def /m { mark } bind def /ru { /dy exch 1 sub neg def /dx exch 1 sub def gsave currentpoint newpath moveto dx 0 rlineto 0 dy rlineto dx neg 0 rlineto closepath fill grestore } bind def /@end { (Time used: ) print usertime StartTime sub @pri (VM used: ) print @VMused @pri (. Unused: ) print vmstatus @VMused sub @pri pop pop (\n) print flush end } def /DraftFirst { gsave initmatrix newpath /Helvetica-Bold findfont setfont (Draft) dup stringwidth pop 8.875 exch div dup 72 mul dup scale 52.3 rotate 2.5 exch div -.35 translate 0.95 setgray 0 0 moveto show grestore } bind def /DraftMore { gsave initmatrix newpath /Helvetica-Bold findfont 72 scalefont setfont 0.95 setgray 576 702 moveto (Draft) stringwidth exch neg exch neg rmoveto (Draft) show grestore } bind def /@draft { /@bop1 { 1 le {DraftFirst} {DraftMore} ifelse Mtrx setmatrix /SaveImage save def } bind def } bind def /@twoup { initmatrix [ 0 1 -1 0 0 0 ] concat 36 -87 translate 5.5 8.5 div dup scale /isoddpage true def /@eop { isoddpage not {showpage} if SaveImage restore /isoddpage isoddpage not def } def /@bop1 { pop isoddpage { SecondMtrx setmatrix } { Mtrx setmatrix } ifelse /SaveImage save def } def /@end { isoddpage not { showpage } if end } def } def /@beginspecial { SpecialDict begin gsave /SpecialSave save def currentpoint transform initgraphics itransform translate 0 0 moveto SpecialDefaults IfMacSetUp } def /@setspecial { hof vof translate setclipper hsc vsc scale angl rotate } def /@endspecial { SpecialSave restore grestore end } def /@beginfullpage { gsave /SpecialSave save def SpecialDict begin /showpage {} def initgraphics } def /@endfullpage { clear end SpecialSave restore grestore showpage } def /SpecialDict 50 dict def SpecialDict begin /Inch { 72 mul} bind def /SpecialDefaults { /hsi 8.5 Inch def /vsi 11 Inch def /hof 0 def /vof 0 def /hsc 1 def /vsc 1 def /angl 0 def /CLIP false def } def /@hsize {/hsi exch def /CLIP true def} def /@vsize {/vsi exch def /CLIP true def} def /@hoffset {/hof exch def} def /@voffset {/vof exch def} def /@hscale {/hsc exch def} def /@vscale {/vsc exch def} def /@rotate {/angl exch def} def /setclipper { CLIP { newpath 0 0 moveto hsi 0 rlineto 0 vsi rlineto hsi neg 0 rlineto closepath clip } if } def end /IfMacSetUp { userdict /md known { userdict /md get type /dicttype eq { md begin /txpose{ 1 -1 scale } bind def /cp {pop pop} bind def end } if } if } def end /TeXDict where {/TeXDict get begin} { (Need to load basic TeXDict first\n) print currentfile flushfile} ifelse /@texmakefont { /TeXsize exch def [ TeXsize 0 0 TeXsize neg 0 0 ] makefont def } bind def /@ps2texfont { dup FontDirectory exch known { exch pop findfont } { ReEncodeForTeX } ifelse exch @texmakefont } bind def /ReEncodeForTeX { /newfontname exch def /basefontname exch def /TeXstr 30 string def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup /FID ne { dup /Encoding eq { exch dup length array copy newfont 3 1 roll put } { exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall basefontdict /MathFontName known not { /TeXvec basefontname TeXstr cvs (Courier) search { pop pop pop TeXcourvec } { pop TeXnormalvec } ifelse def TeXvec aload pop TeXvec length 2 idiv { newfont /Encoding get 3 1 roll put } repeat } if newfontname newfont definefont } bind def /TeXnormalvec [ 8#014 /fi 8#015 /fl 8#020 /dotlessi 8#022 /grave 8#023 /acute 8#024 /caron 8#025 /breve 8#026 /macron 8#027 /ring 8#030 /cedilla 8#031 /germandbls 8#032 /ae 8#033 /oe 8#034 /oslash 8#035 /AE 8#036 /OE 8#037 /Oslash 8#042 /quotedblright 8#074 /exclamdown 8#076 /questiondown 8#134 /quotedblleft 8#136 /circumflex 8#137 /dotaccent 8#173 /endash 8#174 /emdash 8#175 /hungarumlat 8#176 /tilde 8#177 /dieresis ] def /TeXcourvec [ 8#016 /exclamdown 8#017 /questiondown 8#020 /dotlessi 8#022 /grave 8#023 /acute 8#024 /caron 8#025 /breve 8#026 /macron 8#027 /ring 8#030 /cedilla 8#031 /germandbls 8#032 /ae 8#033 /oe 8#034 /oslash 8#035 /AE 8#036 /OE 8#037 /Oslash 8#074 /less 8#076 /greater 8#134 /backslash 8#136 /circumflex 8#137 /underscore 8#173 /braceleft 8#174 /bar 8#175 /braceright 8#177 /dieresis ] def /ObliqueFont { /ObliqueAngle exch def /ObliqueBaseName exch def /ObliqueFontName exch def /ObliqueTransform [1 0 ObliqueAngle sin ObliqueAngle cos div 1 0 0] def /basefontdict ObliqueBaseName findfont ObliqueTransform makefont def /newfont basefontdict maxlength dict def basefontdict { exch dup /FID ne { dup /Encoding eq { exch dup length array copy newfont 3 1 roll put } { exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall newfont /FontName ObliqueFontName put ObliqueFontName newfont definefont pop } bind def /SmallCapsFont { /SmallCapsBaseName exch def /SmallCapsFontName exch def /basefontdict SmallCapsBaseName findfont def /newfont basefontdict maxlength 10 add dict def newfont begin /FontName SmallCapsFontName def /FontBaseDict basefontdict 1000 scalefont def /FontSCDict FontBaseDict .8 scalefont def /FontType 3 def /BuildChar {SmallCapChar} def /FontMatrix dup basefontdict exch get def /FontBBox dup basefontdict exch get def /Encoding dup basefontdict exch get def end SmallCapsFontName newfont definefont pop } bind def /SmallCapChar { /achar (A) def achar exch 0 exch put begin achar 0 get dup 97 ge exch 122 le and { achar 0 achar 0 get 32 sub put FontSCDict } { FontBaseDict } ifelse setfont achar stringwidth FontBBox setcachedevice newpath 0 0 moveto achar show end } bind def /MathEncodingVec [ /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon1 /Phi /Psi /Omega /alpha /beta /gamma /delta /epsilon /zeta /nu /theta /iota /kappa /lambda /mu /nu /xi /pi /rho /sigma /tau /upsilon /phi /chi /psi /omega /epsilon /theta1 /omega1 /rho /sigma /phi1 /arrowleft /arrowleft /arrowright /arrowright /suchthat /congruent /proportional /angle /zero /one /two /three /four /five /six /seven /eight /nine /period /comma /less /slash /greater /asteriskmath /partialdiff /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /registerserif /copyrightserif /trademarkserif /logicalor /logicaland /section /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /dotlessi /j /weierstrass /macron /breve ] def /MathCharVec [ 71 68 81 76 88 80 83 161 70 89 87 97 98 103 100 101 122 110 113 105 107 108 109 110 120 112 114 115 116 117 102 99 121 119 101 74 118 114 115 106 172 172 174 174 39 64 181 208 48 49 50 51 52 53 54 55 56 57 46 44 60 47 62 42 182 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 210 211 212 218 217 167 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 245 106 195 197 198 ] def /MathDictVec [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 ] def /MathOblique { 3 copy ObliqueFont pop pop MathFont } bind def /MathFont { /MathSymName exch def /MathBaseName exch def /MathFontName exch def /basefontdict MathBaseName findfont def /newfont basefontdict maxlength 10 add dict def newfont begin /FontName MathFontName def /FontDictArray [ basefontdict 1000 scalefont MathSymName findfont 950 scalefont /Symbol findfont 950 scalefont ] def /FontType 3 def /BuildChar {MathFontChar} def /FontMatrix dup basefontdict exch get def /FontBBox dup basefontdict exch get def /Encoding dup basefontdict exch get dup length array copy def /WhichFont MathDictVec def /WhichChar MathCharVec def MathEncodingVec Encoding copy pop /achar (A) def end MathFontName newfont definefont pop } bind def /MathFontChar { exch begin achar exch 0 exch put FontDictArray WhichFont achar 0 get get get setfont achar dup 0 get WhichChar exch get 0 exch put achar stringwidth FontBBox setcachedevice newpath 0 0 moveto achar show end } bind def end /psf$TeXscale { 65536 div } def /DocumentInitState [ matrix currentmatrix currentlinewidth currentlinecap currentlinejoin currentdash currentgray currentmiterlimit ] cvx def /startTexFig { /psf$SavedState save def userdict maxlength dict begin currentpoint transform DocumentInitState setmiterlimit setgray setdash setlinejoin setlinecap setlinewidth setmatrix itransform moveto /psf$ury exch psf$TeXscale def /psf$urx exch psf$TeXscale def /psf$lly exch psf$TeXscale def /psf$llx exch psf$TeXscale def /psf$y exch psf$TeXscale def /psf$x exch psf$TeXscale def currentpoint /psf$cy exch def /psf$cx exch def /psf$sx psf$x psf$urx psf$llx sub div def /psf$sy psf$y psf$ury psf$lly sub div def psf$sx psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub translate /DefFigCTM matrix currentmatrix def /initmatrix { DefFigCTM setmatrix } def /defaultmatrix { DefFigCTM exch copy } def /initgraphics { DocumentInitState setmiterlimit setgray setdash setlinejoin setlinecap setlinewidth setmatrix DefFigCTM setmatrix } def /showpage { initgraphics } def /erasepage { initgraphics } def /copypage {} def } bind def /clipFig { currentpoint 6 2 roll newpath 4 copy 4 2 roll moveto 6 -1 roll exch lineto exch lineto exch lineto closepath clip newpath moveto } bind def /doclip { psf$llx 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[<01FCFC03FFFE07FFFC0F03E00E01E00E00E00E00E00E00E00E00E00E00E00E00E00E00E00E00E0 0E00E00E00E00E00E00E00E07E07E0FE0FE07E07E0> 23 20 0 0 24] 117 @dc [<7FC3FCFFE7FE7FC3FC0E00E00E00E00E00E00E00E00E00E00E00E00E00E00E00E00E00E00E00E0 0E00E00F00E00F80E00FC1C07FFFC0FEFF807E3E00> 23 20 0 0 24] 110 @dc [<01FC0007FF001FFF803E03C03801C07001C0700000E00000E00000E00000E00000E00000E00000 7000007000003803003E07801FFF8007FF0001FE00> 18 20 -3 0 24] 99 @dc [ 17 29 -4 0 24] 105 @dc [<01F0000FFE001FFF003E0F803C07807803C07001C0F001E0E000E0E000E0E000E0E000E0E000E0 7001C07001C03803803E0F801FFF000FFE0001F000> 19 20 -2 0 24] 111 @dc [<7FC3FCFFE7FE7FC3FC0E00E00E00E00E00E00E00E00E00E00E00E00E00E00E00E00E00E00E00E0 0E00E00F00E00F80E00FC1C00FFFC00EFF800E3E000E00000E00000E00000E00000E00007E0000 FE00007E0000> 23 28 0 0 24] 104 @dc [ 17 20 -3 0 24] 115 @dc [<007000F001F003C007800F001E001C00380038007000700070007000E000E000E000E000E000E0 00E000E0007000700070007000380038001C001E000F00078003C001E000F00070> 12 36 -7 4 24] 40 @dc [<7F8FF0FF8FF87F8FF00F0780070700038E00039E0001DC0000F80000F00000700000F80001F800 01DC00039E00078E000707007F8FF07F9FF07F8FF0> 21 20 -1 0 24] 120 @dc [<6000F00078003C001E000F000780038001C001C000E000E000E000E00070007000700070007000 700070007000E000E000E000E001C001C0038007800F001E003C007800F0006000> 12 36 -4 4 24] 41 @dc [<7F07F0FF8FF87F07F01C01C01C01C01C01C01C01C01C01C01C01C01C01C01C01C01C01C01C01C0 1FFFC01FFFC01FFFC01C01C01C01C01C01C01C01C01C01C01C01C01C01C01C01C01C01C07F07F0 FF8FF87F07F0> 21 28 -1 0 24] 72 @dc [<0FF8003FFE007FFF00780F00700700F00780E00380E00380E00380E00380E00380E00380E00380 E00380E00380E00380E00380E00380E00380E00380E00380E00380F00780700700780F007FFF00 3FFE000FF800> 17 28 -3 0 24] 79 @dc [<007C0001FF0003FF800783C00F01E00E00E01C00701C00701C00701C00701C00701C00701C0070 1C00701C00701C00701C00701C00701C00701C00701C00701C00701C00701C00701C0070FF83FE FF83FEFF83FE> 23 28 0 0 24] 85 @dc [ 19 28 -2 0 24] 83 @dc [ 21 28 -1 0 24] 69 @dc [<7F1F1F00FFBFBF807F1F1F001C1C1C001C1C1C001C1C1C001C1C1C001C1C1C001C1C1C001C1C1C 001C1C1C001C1C1C001C1C1C001C1C1C001E1E1C001E1E1C001F1F1C007FFFF800FFFBF8007CE0 E000> 25 20 1 0 24] 109 @dc [<7FC000FFE0007FC0000E00000E00000E00000E00000E00000E00000E00000E3E000EFF800FFFC0 0FC1E00F80E00F00700F00700E00380E00380E00380E00380E00380E00380E00700F00700F80E0 0FC1E07FFFC0FEFF807E3E00> 21 30 0 10 24] 112 @dc [<7FFFC0FFFFE07FFFC000E00000E00000E00000E00000E00000E00000E00000E00000E00000E000 00E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E0007FE000 FFE0007FE000> 19 28 -2 0 24] 108 @dc [<03E3F00FFBF81FFFF03C1F80380F80700780700780E00380E00380E00380E00380E00380E00380 700380700780380F803C1F801FFF800FFB8003E380000380000380000380000380000380001F80 003F80001F80> 21 28 -2 0 24] 100 @dc [<7FFE00FFFF007FFE0003800003800003800003800003800003800003800003800003800003C000 03C00003E00003F03003F8787FBFF8FF9FF07F87E0> 21 20 -1 0 24] 114 @dc [ 20 20 -1 0 24] 122 @dc [<60C0F1F0FBF83FBE1F1E060C> 15 6 -4 -22 24] 126 @dc [<01F00007FC000FFE001F1F001C07003803807803C07001C07001C0F001E0E000E0E000E0E000E0 E000E0E000E0E000E0E000E0E000E0E000E07001C07001C07803C03803801C07001F1F000FFE00 07FC0001F000> 19 28 -2 0 24] 48 @dc [<60F87C1E0E071F3F7F7E3E1C> 8 12 -8 6 24] 44 @dc [<7FFCFFFE7FFC038003800380038003800380038003800380038003800380038003800380038043 80FB80FF803F800F800780038003800180> 15 28 -5 0 24] 49 @dc [<01FC000FFF801FFFC07E03F07800F0E00038E00038E00038E000387000707801F03FFFE01FFFC0 1FFE001C000038000039E0001FF8001FFC001E1E001C0E00380700380700380700380700380700 1C0E001E1E300FFFF807FFF801E1F0> 21 31 -1 11 24] 103 @dc [<7FFFE0FFFFE07FFFE03C00E01E00E00F800007C00001E00000F000007800003C00001E00000F00 0007800003C00001C00001C00000E00000E06000E0F000E0F000E0E001C07003C07C0F803FFF00 0FFE0003F000> 19 28 -2 0 24] 50 @dc [<3078FCFC783000000000000000003078FCFC7830> 6 20 -9 0 24] 58 @dc [<600000F00000F00000F800007800007C00003C00003C00003E00001E00001F00000F00000F0000 0F800007800007C00003C00003C00003E00001E00001F00000F00000F800007800007800007C00 003C00003E00001E00001E00001F00000F00000F80000780000780000300> 17 36 -3 4 24] 47 @dc 21 @bop1 cmsl10.329 @sf 60 -99 p m (The) 15 (Generalized) 17 (QR) 16 (Decomp) 1 (osition) ks cmr10.329 @sf 1037 r m (21) s cmtt10.329 @sf 251 45 p m (w) 24 (=) 23 (beta*A*v;) ks 251 102 p m (A) 24 (=) 23 (A) 24 (+) 24 (w*v';) ks 60 158 p m (%) s 251 214 p m (function) 23 (v) 23 (=) 24 (house\(x\)) ks 60 271 p m (%) s 60 327 p m (%) 167 (HOUSE) 23 (computes) 23 (the) 23 (Householdr) 23 (vectors) ks 60 384 p m (%) s 275 440 p m (n) 23 (=) 24 (max\(size\(x\)\);) ks 275 497 p m (mu) 23 (=) 24 (norm\(x\);) ks 275 553 p m (v) 23 (=) 24 (x;) ks 275 610 p m (if) 23 (mu) 24 (~=) 24 (0,) ks 346 666 p m (beta) 24 (=) 23 (x\(1\)) 24 (+) 23 (sign\(x\(1\)\)*mu;) ks 346 723 p m (v\(2:n\)) 23 (=) 24 (v\(2:n\)/beta;) ks 275 779 p m (end) s 275 835 p m (v\(1\)) 23 (=) 24 (1;) ks @eop 20 @bop0 cmtt10.329 @sf [<07FF0007FF0007FF00007000007000007000007000007000007000007000007000007000007000 007000007000007000007000007000007000007000007000E07038E07038E07038E07038FFFFF8 FFFFF87FFFF8> 21 28 -1 0 24] 84 @dc [ 21 28 -1 0 24] 107 @dc [<3078FCFC7830> 6 6 -9 0 24] 46 @dc [<7FFF00FFFF80FFFF807FFF00> 17 4 -3 -12 24] 45 @dc [<000700000700000F00000E00001E00001C000FFC003FFE007FFF00787F0070F700F0E780E1E380 E1E380E00380E00380E00380E00380E00380E00380E00380E00380E00380E00380E00380E00380 E00380E00380F00780700700780F007FFF003FFE000FF800> 17 34 -3 6 24] 81 @dc [<7F00F0FF81F87F01F81C039C1C039C1C039C1C03801C03801C03801C03801C03801C07001C0F00 1FFE001FFE001FFF001C0F801C03801C03C01C01C01C01C01C01C01C03C01C03801C0F807FFF00 FFFE007FF800> 22 28 -1 0 24] 82 @dc [ 20 28 -1 0 24] 80 @dc [ 20 28 -1 0 24] 66 @dc [<00700000F80000F80000D80001DC0001DC0001DC00018C00038E00038E00038E00038E00070700 0707000707000707000F07800E03800E03800E03800E03801C01C01C01C01C01C01C01C0FF07F8 FF07F8FF07F8> 21 28 -1 0 24] 86 @dc [ 13 36 -9 4 24] 91 @dc [ 13 36 -1 4 24] 93 @dc [<003FF8003FF8003FF800038000038000038000038000038000038000038003E3800FFB801FFF80 3C1F80380F80700780700780E00380E00380E00380E00380E00380E00380700780700780380F80 3E1F801FFF8007FB8001E380> 21 30 -2 10 24] 113 @dc [<00F80003FE0007FF800F07C01E01C03C00E03800E07000E07000E0700000E00000E00000E00000 E00000E00000E00000E00000E000007000007000E07000E03800E03C01E01E03E00F07E007FFE0 03FEE000F8E0> 19 28 -2 0 24] 67 @dc [<1E00003F00007F80007BC00079E00000E00000F000007000007000007000007800007800007800 00DC0000CC0000CC0001CE0001CE00038E000386000387000707000707000703800E03800E0380 0E01C07F8FF0FF8FF87F8FF0> 21 30 -1 10 24] 121 @dc [<000300000780001F80003F00007E0001FC0003F00007E0001FC0003F00007E0000FC0000FC0000 7E00003F00001FC00007E00003F00001FC00007E00003F00001F80000780000300> 17 24 -3 -2 24] 60 @dc 20 @bop1 cmsl10.329 @sf 60 -99 p m (The) 15 (Generalized) 17 (QR) 16 (Decomp) 1 (osition) ks cmr10.329 @sf 1037 r m (20) s cmtt10.329 @sf 60 45 p m (%) s 60 102 p m (%) 167 (Test) 23 (the) 24 (backward) 22 (error) 24 (if) 23 (wanted.) ks 60 158 p m (%) s 251 214 p m (resida) 23 (=) 24 (norm\(A) 23 (-) 23 (Q*R*P'\)) ks 251 271 p m (residb) 23 (=) 24 (norm\(B) 23 (-) 23 (Q*S*V'\)) ks 251 495 p m (function) 23 ([R,Q]) 23 (=) 24 (rq\(A\)) ks 60 552 p m (%) s 60 608 p m (%) 48 (RQ) 47 (-------------------) -1 (-------) -1 (--------) -1 (-------) -1 (-------) -1 (-------) -1 (----) ks 60 665 p m (%) s 60 721 p m (%) 215 (Compute) 23 (RQ) 23 (decomposition) 22 (of) 24 (matrix) 23 (A.) ks 60 778 p m (%) s 60 834 p m (%) 549 (A) 23 (=) 24 (R*Q) ks 60 890 p m (%) s 60 947 p m (%) 48 (----------------) -1 (-------) -1 (-------) -1 (--------) -1 (-------) -1 (-------) -1 (-------) -1 (----) ks 60 1003 p m (%) s 251 1060 p m ([n,m]) 23 (=) 24 (size\(A\);) ks 251 1116 p m (Q) 24 (=) 23 (eye\(m\);) ks 60 1173 p m (%) s 322 1229 p m (if) 24 (n) 24 (<=) 23 (m) ks 394 1286 p m (for) 24 (i) 23 (=) 24 (n:-1:1) ks 466 1342 p m (x) 23 (=) 24 (A\(i,1:m-n+i\);) ks 466 1399 p m (v) 23 (=) 24 (housen\(x\);) ks 466 1455 p m (v) 23 (=) 24 (v';) ks 466 1511 p m (A\(1:i,1:m-n+i\)) 22 (=) 23 (colhouse\(A\(1:i,1:m-n+) -1 (i\),v\);) ks 466 1568 p m (Q\(1:m,1:m-n+i\)) 22 (=) 23 (colhouse\(Q\(1:m,1:m-n+) -1 (i\),v\);) ks 394 1624 p m (end) s 322 1681 p m (else) s 394 1737 p m (for) 24 (i) 23 (=) 24 (n:-1:n-m+2) ks 466 1794 p m (x) 23 (=) 24 (A\(i,1:m-n+i\);) ks 466 1850 p m (v) 23 (=) 24 (housen\(x\);) ks 466 1907 p m (v) 23 (=) 24 (v';) ks 466 1963 p m (A\(1:i,1:m-n+i\)) 22 (=) 23 (colhouse\(A\(1:i,1:m-n+) -1 (i\),v\);) ks 466 2020 p m (Q\(1:m,1:m-n+i\)) 22 (=) 23 (colhouse\(Q\(1:m,1:m-n+) -1 (i\),v\);) ks 394 2076 p m (end) s 322 2132 p m (end) s 60 2189 p m (%) s 251 2245 p m (R) 24 (=) 23 (A;) ks 251 2302 p m (Q) 24 (=) 23 (Q';) ks 60 2358 p m (%) s 251 2415 p m (function) 23 (A) 23 (=) 24 (colhouse\(A,v\)) ks 60 2471 p m (%) s 60 2528 p m (%) 167 (Apply) 23 (the) 24 (Householder) 22 (matrix) 23 (from) 23 (right) 23 (left) ks 60 2584 p m (%) 262 (A) 24 (<==) 24 (A*H) ks 60 2641 p m (%) s 251 2697 p m (beta) 23 (=) 24 (-2/\(v'*v\);) ks @eop 19 @bop0 cmtt10.329 @sf [<600000F00000FC00007E00003F00001FC00007E00003F00001FC00007E00003F00001F80001F80 003F00007E0001FC0003F00007E0001FC0003F00007E0000FC0000F00000600000> 17 24 -3 -2 24] 62 @dc [ 21 28 -1 0 24] 77 @dc 19 @bop1 cmsl10.329 @sf 60 -99 p m (The) 15 (Generalized) 17 (QR) 16 (Decomp) 1 (osition) ks cmr10.329 @sf 1037 r m (19) s cmtt10.329 @sf 60 45 p m (%) 167 (else) 23 (if) 24 (n) 24 (>) 23 (p,) 24 (then) ks 60 102 p m (%) s 60 158 p m (%) 334 (S) 24 (=) 23 ([) 24 (S11) 24 (S12) 23 (]) 24 (q) ks 60 214 p m (%) 429 ([) 48 (0) 48 (S22) 23 (]) 24 (k) ks 60 271 p m (%) 429 ([) 48 (0) 71 (0) 48 (]) 24 (n-q-k) ks 60 327 p m (%) 429 (p-n+q) 47 (n-q) ks 60 384 p m (%) s 60 440 p m (%) 167 (where) 23 (S21\(kxp\)) 23 (is) 23 (full) 24 (row) 23 (rank) 24 (upper) 23 (trapezoidal) 22 (form.) ks 60 497 p m (%) s 60 553 p m (%) 48 (----------------) -1 (-------) -1 (-------) -1 (--------) -1 (-------) -1 (-------) -1 (-------) -1 (------) ks 60 610 p m (%) s 251 666 p m ([n,m]) 23 (=) 24 (size\(A\);) ks 251 723 p m ([n1,p]) 23 (=) 24 (size\(B\);) ks 60 779 p m (%) s 251 835 p m (if) 23 (n1) 24 (~=) 24 (n) ks 322 892 p m (error\('Matrices) 22 (A) 24 (and) 23 (B) 24 (have) 24 (different) 22 (rows'\)) ks 251 948 p m (end) s 60 1005 p m (%) s 60 1061 p m (%) 167 (QR) 23 (decomposition) 23 (with) 23 (column) 23 (pivoting) 23 (of) 23 (A:) ks 60 1118 p m (%) 549 (Q'*A*P) 23 (=) 23 (R) ks 60 1174 p m (%) s 251 1231 p m ([Q,R,P]) 23 (=) 24 (qr\(A\);) ks 251 1287 p m (q) 24 (=) 23 (rank\(R\);) ks 60 1344 p m (%) s 251 1400 p m (if) 23 (n<=) 24 (p) ks 322 1456 p m ([S,V]) 24 (=) 23 (rq\(Q'*B\);) ks 322 1513 p m (V) 24 (=) 24 (V';) ks 322 1569 p m ([Q1,S\(q+1:n,p-n+q+1:p\)) -1 (,P1]) 22 (=) 24 (qr\(S\(q+1:n,p-n+) -1 (q+1:p\)\)) -1 (;) ks 322 1626 p m (S\(1:q,p-n+q+1:p\)) 22 (=) 24 (S\(1:q,p-n+q+1:p\)*P) -1 (1;) ks 322 1682 p m (Q\(1:n,q+1:n\)) 23 (=) 23 (Q\(1:n,q+1:n\)*Q1;) ks 322 1739 p m (V\(1:p,p-n+q+1:p\)) 22 (=) 24 (V\(1:p,p-n+q+1:p\)*P) -1 (1;) ks 60 1795 p m (%) s 251 1852 p m (else) 71 (%) 24 (n) 23 (>) 24 (p) 24 (case) ks 322 1908 p m (if) 24 (p) 24 (<=) 23 (n-q) ks 394 1965 p m (S) 24 (=) 24 (Q'*B;) ks 394 2021 p m ([Q1,S\(q+1:n,1:p\),P1) -1 (]) 22 (=) 24 (qr\(S\(q+1:n,1:p\)\);) ks 394 2077 p m (S\(1:q,1:p\)) 23 (=) 23 (S\(1:q,1:p\)*P1;) ks 394 2134 p m (Q\(1:n,q+1:n\)) 22 (=) 24 (Q\(1:n,q+1:n\)*Q1;) ks 394 2190 p m (V) 24 (=) 24 (P1;) ks 322 2247 p m (else) 48 (%) 23 (p) 24 (>) 24 (n-q) ks 394 2303 p m ([S,V]) 23 (=) 24 (rq\(Q'*B\);) ks 394 2360 p m (V) 24 (=) 24 (V';) ks 394 2416 p m ([Q1,S\(q+1:n,p-\(n-q\)) -1 (+1:p\),P1) -1 (]) 22 (=) 24 (qr\(S\(q+1:n,p-\(n-q) -1 (\)+1:p\)\);) ks 394 2473 p m (S\(1:q,p-\(n-q\)+1:p\)) 45 (=) 24 (S\(1:q,p-\(n-q\)+1:p\)*) -1 (P1;) ks 394 2529 p m (Q\(1:n,q+1:n\)) 22 (=) 24 (Q\(1:n,q+1:n\)*Q1;) ks 394 2586 p m (V\(1:p,p-\(n-q\)+1:p\)) 21 (=) 24 (V\(1:p,p-\(n-q\)+1:p\)*P) -1 (1;) ks 322 2642 p m (end) s 251 2698 p m (end) s @eop 18 @bop0 cmtt10.329 @sf [<01F1C003FDC00FFFC01F0FC01C07C03803C03803C07003C07001C07001C0E00FF0E01FF0E00FF0 E00000E00000E00000E00000E000007000007001C07001C03801C03803C01C03C01F0FC00FFFC0 03FDC001F1C0> 20 28 -2 0 24] 71 @dc [ 19 28 -2 0 24] 70 @dc 18 @bop1 cmsl10.329 @sf 60 -99 p m (The) 15 (Generalized) 17 (QR) 16 (Decomp) 1 (osition) ks cmr10.329 @sf 1037 r m (18) s cmtt10.329 @sf 322 45 p m (error\('suggest) 22 (to) 24 (use) 23 (GQR) 24 (factorization'\)) ks 251 102 p m (end) s 60 158 p m (%) s 60 214 p m (%) 167 (QR) 23 (decomposition) 23 (of) 23 (B:) ks 60 271 p m (%) 549 (Q'*B) 23 (=) 24 (S) ks 60 327 p m (%) s 251 384 p m ([Q,S]) 23 (=) 24 (qr\(B\);) ks 60 440 p m (%) s 60 497 p m (%) 167 (RQ) 23 (decomposition) 23 (of) 23 (Q'*A:) ks 60 553 p m (%) 549 (Q'*A) 23 (=) 24 (R*U;) ks 60 610 p m (%) s 251 666 p m ([R,U]) 23 (=) 24 (rq\(Q'*A\);) ks 60 723 p m (%) s 60 779 p m (%) 167 (Test) 23 (the) 24 (backward) 22 (error) ks 60 835 p m (%) s 251 892 p m (resida) 23 (=) 24 (norm\(A) 23 (-) 23 (Q*R*U\)) ks 251 948 p m (residb) 23 (=) 24 (norm\(B) 23 (-) 23 (Q*S\)) ks 251 1173 p m (function) 23 ([Q,P,V,R,S]) 22 (=) 24 (gqrp\(A,B\)) ks 60 1229 p m (%) s 60 1286 p m (%) 48 (GQRP) 23 (------------------) -1 (-------) -1 (--------) -1 (-------) -1 (-------) -1 (-------) -1 (------) ks 60 1342 p m (%) s 60 1399 p m (%) 167 (Generalized) 22 (QR) 24 (factorization) 22 (with) 23 (partial) 23 (pivoting) 23 (of) ks 60 1455 p m (%) 167 (matrices) 23 (A\(nxm\)) 23 (and) 23 (B\(nxp\).) ks 60 1511 p m (%) s 60 1568 p m (%) 167 (Find) 23 (orthogonal) 23 (matrices) 22 (Q,) 24 (V) 24 (and) 23 (permutation) 23 (matrix) 23 (P) ks 60 1624 p m (%) 167 (such) 23 (that) ks 60 1681 p m (%) s 60 1737 p m (%) 358 (A) 24 (=) 23 (Q*R*P';) 119 (B) 23 (=) 24 (Q*S*V';) ks 60 1794 p m (%) s 60 1850 p m (%) 167 (where) ks 60 1907 p m (%) s 60 1963 p m (%) 334 (R) 24 (=) 23 ([) 24 (R11) 24 (R12) 23 (]) 24 (q) ks 60 2020 p m (%) 429 ([) 48 (0) 71 (0) 48 (]) 24 (n-q) ks 60 2076 p m (%) 525 (q) 47 (m-q) ks 60 2132 p m (%) s 60 2189 p m (%) 167 (R11\(qxq\)) 23 (is) 23 (nonsingular) 23 (upper) 23 (trinagular,) ks 60 2245 p m (%) 167 (and) 23 (if) 24 (n) 24 (<=) 23 (p,) 24 (then) ks 60 2302 p m (%) s 60 2358 p m (%) 334 (S) 24 (=) 23 ([) 48 (0) 48 (S11) 23 (S12) 47 (]) 24 (q) ks 60 2415 p m (%) 429 ([) 48 (0) 71 (0) 48 (S22) 47 (]) 24 (k) ks 60 2471 p m (%) 429 ([) 48 (0) 71 (0) 72 (0) 71 (]) 24 (n-k-q) ks 60 2528 p m (%) 477 (p-n) 47 (q) 48 (n-q) ks 60 2584 p m (%) s 60 2641 p m (%) 167 (S22\(kx\(n-q\)\)) 22 (is) 24 (full) 23 (row) 23 (rank) 24 (upper) 23 (trapezoidal,) 22 (if) 24 (exists.) ks 60 2697 p m (%) s @eop 17 @bop0 17 @bop1 cmsl10.329 @sf 60 -99 p m (The) 15 (Generalized) 17 (QR) 16 (Decomp) 1 (osition) ks cmr10.329 @sf 1037 r m (17) s cmtt10.329 @sf 60 45 p m (%) s 60 102 p m (%) 167 (RQ) 23 (factorization) 23 (of) 23 (Q'*B:) ks 60 158 p m (%) 549 (Q'*B) 23 (=) 24 (S*V;) ks 60 214 p m (%) s 251 271 p m ([S,V]) 23 (=) 24 (rq\(Q'*B\);) ks 60 327 p m (%) s 60 384 p m (%) 167 (Test) 23 (the) 24 (backward) 22 (error) ks 60 440 p m (%) s 251 497 p m (resida) 23 (=) 24 (norm\(A) 23 (-) 23 (Q*R\)) ks 251 553 p m (residb) 23 (=) 24 (norm\(B) 23 (-) 23 (Q*S*V\)) ks 251 778 p m (function) 23 ([Q,U,R,S]) 22 (=) 24 (grq\(A,B\)) ks 60 834 p m (%) s 60 890 p m (%) 48 (GRQ) 23 (-------------------) -1 (-------) -1 (--------) -1 (-------) -1 (-------) -1 (-------) -1 (--) ks 60 947 p m (%) s 60 1003 p m (%) 167 (Compute) 23 (the) 23 (generalized) 23 (RQ) 23 (factorization) 22 (of) 24 (A\(nxm\)) 23 (and) ks 60 1060 p m (%) 167 (B\(nxp\):) ks 60 1116 p m (%) s 60 1173 p m (%) 358 (A) 24 (=) 23 (Q*R;) 191 (B) 23 (=) 24 (Q*S*V;) ks 60 1229 p m (%) s 60 1286 p m (%) 167 (where) 23 (n) 24 (<=) 23 (m,) 24 (Q\(nxn\),) 23 (V\(pxp\)) 23 (are) 23 (orthogonal) 23 (matrices,) ks 60 1342 p m (%) 167 (R) 24 (and) 23 (S) 24 (assumes) 23 (one) 23 (of) 24 (the) 23 (forms:) ks 60 1399 p m (%) 167 (if) 23 (n) 24 (<=) 24 (p) ks 60 1455 p m (%) s 60 1511 p m (%) 358 (R) 24 (=) 23 ([) 24 (0) 48 (R11) 23 (]) 24 (n) 214 (S) 24 (=) 24 ([) 24 (S11) 23 (S12) 23 (]) 24 (n) ks 60 1568 p m (%) 477 (m-n) 47 (n) 501 (n) 48 (p-n) ks 60 1624 p m (%) s 60 1681 p m (%) 167 (if) 23 (n) 24 (>) 24 (p) ks 60 1737 p m (%) s 60 1794 p m (%) 358 (R) 24 (=) 23 ([) 24 (0) 48 (R11) 23 (]) 24 (n) 214 (S) 24 (=) 24 ([) 24 (S11) 23 (]) 24 (p) ks 60 1850 p m (%) 477 (m-n) 47 (n) 430 ([) 47 (0) 48 (]) 24 (n-p) ks 60 1907 p m (%) 1121 (p) ks 60 1963 p m (%) s 60 2020 p m (%) 167 (where) 23 (n) 24 (by) 23 (n) 24 (matrix) 23 (R11) 24 (and) 23 (min\(n,p\)) 23 (by) 23 (min\(n,p\)) 23 (matrix) ks 60 2076 p m (%) 167 (S11) 23 (are) 24 (upper) 23 (triangular.) ks 60 2132 p m (%) s 60 2189 p m (%) 48 (----------------) -1 (-------) -1 (-------) -1 (--------) -1 (-------) -1 (-------) -1 (-------) -1 (--) ks 60 2245 p m (%) s 251 2302 p m ([n,m]) 23 (=) 24 (size\(A\);) ks 251 2358 p m ([n1,p]) 23 (=) 24 (size\(B\);) ks 60 2415 p m (%) s 251 2471 p m (if) 23 (n1) 24 (~=) 24 (n) ks 322 2528 p m (error\('Matrices) 22 (A) 24 (and) 23 (B) 24 (have) 24 (different) 22 (rows'\)) ks 251 2584 p m (end) s 60 2641 p m (%) s 251 2697 p m (if) 23 (n) 24 (>) 24 (m) ks @eop 16 @bop0 cmbx10.432 @sf [ 47 41 -2 0 52] 65 @dc [ 58 41 -3 0 65] 77 @dc [<01FC03FC0FFF0FFC3F839FFC7F00DF807E007F80FE003F80FE003F80FE003F80FE003F807F003F 803F003F803F803F800FE03F8007FC3F8000FFFF80000FFF8000003F8000003F8000003F800700 3F800F803F801FC03F001FC07E001FC07E000F81F80007FFF00001FF8000> 30 27 -2 0 33] 97 @dc [<001F8000FFC001F86003F87003F03807F03807F03807F03807F03807F03807F03807F00007F000 07F00007F00007F00007F00007F00007F00007F00007F00007F00007F00007F000FFFFF0FFFFF0 1FFFF007F00003F00003F00001F00000F00000F00000F000007000007000007000007000> 21 38 -1 0 27] 116 @dc [ 15 42 -3 0 20] 108 @dc [<0E01FC00000F07FF80000F9E07E0000FF803F0000FF001F8000FE000FC000FE000FE000FE0007F 000FE0007F000FE0007F000FE0007F800FE0007F800FE0007F800FE0007F800FE0007F800FE000 7F800FE0007F800FE0007F000FE0007F000FE0007F000FE000FE000FE000FC000FF000F8000FF8 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[<003FC3FF8000FFF3FF8003F03BFF8007C00FF8000F8007F8001F8003F8003F8003F8007F0003F8 007F0003F8007F0003F800FF0003F800FF0003F800FF0003F800FF0003F800FF0003F800FF0003 F800FF0003F8007F0003F8007F0003F8007F0003F8003F8003F8001F8003F8000FC007F80007E0 0FF80003F03FF80000FFFBF800001FE3F800000003F800000003F800000003F800000003F80000 0003F800000003F800000003F800000003F800000003F800000003F800000003F800000003F800 00003FF80000003FF80000003FF800> 33 42 -2 0 38] 100 @dc 16 @bop1 cmsl10.329 @sf 60 -99 p m (The) 15 (Generalized) 17 (QR) 16 (Decomp) 1 (osition) ks cmr10.329 @sf 1037 r m (16) s cmbx10.432 @sf 60 45 p m (A) s 181 45 p m (Matlab) 23 (Co) 2 (des) ks cmr10.329 @sf 60 155 p m (In) 18 (this) 17 (app) 1 (endix,) 19 (w) 0 (e) 16 (list) 17 (the) 17 (MA) -3 (TLAB) 17 (co) 1 (des) 17 (for) 17 (computing) 17 (the) 17 (GQR) 18 (factorizations) 17 (with) ks 60 211 p m (and) 15 (without) 16 (piv) 0 (oting.) ks cmtt10.329 @sf 251 326 p m (function) 23 ([Q,V,R,S]) 22 (=) 24 (gqr\(A,B\)) ks 60 382 p m (%) s 60 439 p m (%) 48 (GQR) 23 (-------------------) -1 (-------) -1 (--------) -1 (-------) -1 (-------) -1 (-------) -1 (---) ks 60 495 p m (%) s 60 552 p m (%) 167 (Compute) 23 (the) 23 (generalized) 23 (QR) 23 (factorization) 22 (of) 24 (A\(nxm\)) 23 (and) ks 60 608 p m (%) 167 (B\(nxp\):) ks 60 665 p m (%) s 60 721 p m (%) 358 (A) 24 (=) 23 (Q*R;) 191 (B) 23 (=) 24 (Q*S*V;) ks 60 778 p m (%) s 60 834 p m (%) 167 (where) 23 (n) 24 (>=) 23 (m,) 24 (Q\(nxn\),) 23 (V\(pxp\)) 23 (are) 23 (orthogonal) 23 (matrices,) ks 60 890 p m (%) 167 (R) 24 (and) 23 (S) 24 (assumes) 23 (one) 23 (of) 24 (the) 23 (forms:) ks 60 947 p m (%) 167 (if) 23 (n) 24 (<=) 24 (p) ks 60 1003 p m (%) s 60 1060 p m (%) 358 (R) 24 (=) 23 ([) 24 (R11) 23 (]) 24 (m) 215 (S) 24 (=) 23 ([) 24 (0) 48 (S11) 23 (]) 24 (n) ks 60 1116 p m (%) 453 ([) 48 (0) 47 (]) 24 (n-m) 286 (p-n) 47 (n) ks 60 1173 p m (%) 525 (m) ks 60 1229 p m (%) 167 (where) 23 (m) 24 (by) 23 (m) 24 (matrix) 23 (R11) 24 (and) 23 (n) 24 (by) 23 (n) 24 (matrix) 23 (S11) 24 (are) 23 (upper) ks 60 1286 p m (%) 167 (triangular,) 22 (and) ks 60 1342 p m (%) 167 (if) 23 (n) 24 (>) 24 (p) ks 60 1399 p m (%) s 60 1455 p m (%) 358 (R) 24 (=) 23 ([) 24 (R11) 23 (]) 24 (m) 215 (S) 24 (=) 23 ([) 24 (S11) 23 (]) 24 (n-p) ks 60 1511 p m (%) 453 ([) 48 (0) 47 (]) 24 (n-m) 262 ([) 24 (S21) 23 (]) 24 (p) ks 60 1568 p m (%) 525 (m) 501 (p) ks 60 1624 p m (%) 167 (where) 23 (m) 24 (by) 23 (m) 24 (matrix) 23 (R11) 24 (and) 23 (p) 24 (by) 23 (p) 24 (matrix) 23 (S21) 24 (are) 23 (upper) ks 60 1681 p m (%) 167 (triangular.) ks 60 1737 p m (%) s 60 1794 p m (%) 48 (----------------) -1 (-------) -1 (-------) -1 (--------) -1 (-------) -1 (-------) -1 (-------) -1 (---) ks 60 1850 p m (%) s 251 1907 p m ([n,m]) 23 (=) 24 (size\(A\);) ks 251 1963 p m ([n1,p]) 23 (=) 24 (size\(B\);) ks 60 2019 p m (%) s 251 2076 p m (if) 23 (n1) 24 (~=) 24 (n) ks 322 2132 p m (error\('Matrices) 22 (A) 24 (and) 23 (B) 24 (have) 24 (different) 22 (rows'\)) ks 251 2189 p m (end) s 60 2245 p m (%) s 251 2302 p m (if) 23 (n) 24 (<) 24 (m) ks 322 2358 p m (error\('suggest) 22 (to) 24 (use) 23 (GRQ) 24 (factorization'\)) ks 251 2415 p m (end) s 60 2471 p m (%) s 60 2528 p m (%) 167 (QR) 23 (factorization) 23 (of) 23 (A:) ks 60 2584 p m (%) 549 (Q'*A) 23 (=) 24 (RA) ks 60 2640 p m (%) s 251 2697 p m ([Q,R]) 23 (=) 24 (qr\(A\);) ks @eop 15 @bop0 1.000000 /cmmi10.329 @newfont cmmi10.329 @sf [ 30 32 -2 0 34] 65 @dc 1.000000 /cmr8.300 @newfont cmr8.300 @sf [<003000003000003000003000003000003000003000003000003000003000003000FFFFFCFFFFFC 003000003000003000003000003000003000003000003000003000003000003000> 22 24 -2 4 27] 43 @dc 1.000000 /cmmi8.300 @newfont cmmi8.300 @sf [ 15 23 -2 0 15] 73 @dc [ 24 23 -1 0 27] 66 @dc cmmi10.329 @sf [<80700040F80061FC003F060010030008010004008002000001000000C000006000001000000800 0004000002000801000C1F8007F8C003F04001E020> 19 20 -2 0 21] 122 @dc cmr10.329 @sf [<7FFFFFE0FFFFFFF000000000000000000000000000000000000000000000000000000000000000 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@dc cmr10.329 @sf [<7FE7FE0700E00700E00700E00700E00700E00700E00700E00700E00700E00700E00700E00700E0 0700E00700E00700E00700E00700E00700E0FFFFE00700E00700E00700E00700E00700E00700E0 0700E00700E00381E001C1E000E0E0003FE0> 23 32 0 0 25] 13 @dc cmmi10.329 @sf [<3C0000620000F3000079800031800001C00000C00000E00000E00000E00000E000007000007000 007000007000007000003800003800003800003800003800001C00001C00001C00001C00001C00 000E00000E0000FFF0000E00000E00000E0000070000070000070000070000030C00039E00019E 0000CE00007C> 23 41 -2 9 22] 102 @dc [<0F00188038403820382038201C101C001C001C000E000E000E000E0007000700070007000380FF F80380038001C001C001C001C000E000C0> 13 28 -1 0 16] 116 @dc [<40201010080804040474FCFCF870> 6 14 -4 9 13] 59 @dc [<07C018383004700270017000F000F000F000F0007C007BF0780C38023C011C010E01070101C200 7C> 16 20 -2 0 21] 101 @dc [ 31 31 -2 0 34] 66 @dc [<0F0780308C40705C40703C20F01C20F01C20F00E10F00E00F00E00F00E00780700780700780700 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(\000) s cmmi10.329 @sf 10 r m (S) s cmr8.300 @sf 1086 109 p m (12) s cmmi10.329 @sf 1124 102 p m (S) s cmsy8.300 @sf 1155 84 p m (\000) s cmr8.300 @sf m (1) s 1152 114 p m (22) s cmmi10.329 @sf 1201 102 p m (Q) s cmr8.300 @sf 1237 84 p m (T) s 1237 113 p m (2) s cmmi10.329 @sf 1265 102 p m (z) s cmr10.329 @sf 2 r m (\)) s cmmi10.329 @sf m (:) s cmr10.329 @sf 60 185 p m (Hence,) 19 (w) 0 (e) 17 (can) 18 (just) 17 (use) 18 (triangular) 18 (system) 18 (solv) 0 (er) 17 (and) 18 (matrix-v) 0 (ector) 16 (op) 1 (erations) 18 (to) 17 (giv) 0 (e) 17 (the) ks 60 241 p m (estimation) 15 (of) 15 (condition) 17 (n) 0 (um) 0 (b) 1 (ers) 13 (of) 15 (the) 15 (Problem) 16 (GLM.) ks cmbx12.300 @sf 60 371 p m (5.3) s 188 371 p m (Other) 18 (p) 2 (ossible) 17 (applications:) ks cmr10.329 @sf 60 466 p m (Will) 17 (brie\015y) 16 (men) 0 (tion) 15 (the) 15 (p) 1 (ossible) 17 (use) 15 (of) 15 (GQR) 16 (in) ks 131 530 p m (Prepro) 1 (cessing) 16 (step) 15 (of) 15 (computing) 15 (the) 16 (generalized) 17 (singular) 16 (v) -2 (alue) 15 (decomp) 1 (osition.) ks 131 595 p m (Structural) 15 (equations:) ks cmmi10.329 @sf 613 697 p m (f) s cmr10.329 @sf 18 r m (=) s cmmi10.329 @sf 13 r m (A) s cmr8.300 @sf 735 679 p m (T) s cmmi10.329 @sf 762 697 p m (t;) 59 (e) ks cmr10.329 @sf 12 r m (=) s cmmi10.329 @sf 13 r m (B) 2 (B) ks cmr8.300 @sf 1003 679 p m (T) s cmmi10.329 @sf 1032 697 p m (t;) 58 (e) ks cmr10.329 @sf 13 r m (=) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf m (Ad;) s cmr10.329 @sf 60 799 p m (where) s cmmi10.329 @sf 15 r m (f) s cmr10.329 @sf 21 r m (is) 15 (giv) 0 (en,) 15 (and) 15 (w) 0 (e) 14 (wish) 16 (to) 14 (\014nd) ks cmmi10.329 @sf 16 r m (d) s cmr10.329 @sf m (.) s @eop 14 @bop0 cmr10.329 @sf [<000600000006000000060000000600000006000000060000000600000006000000060000000600 000006000000060000000600000006000000060000FFFFFFF0FFFFFFF000060000000600000006 000000060000000600000006000000060000000600000006000000060000000600000006000000 0600000006000000060000> 28 32 -3 5 35] 43 @dc cmmi10.329 @sf [ 32 31 -2 0 34] 69 @dc [ 32 31 -2 0 29] 70 @dc [<1801E03803101C03081C07081C07041C03840E03820E01C00E01C00E01C00700E00700E00700E0 8700E043807043807043C07023A0602318C01E0780> 23 20 -2 0 27] 110 @dc [<1801800F0038038018801C01C018401C01C038401C01C038201C01C01C200E00E01C100E00E00E 000E00E00E000E00E00E0007007007000700700700070070070087007007004380380380438038 038043C034030023A032030023186186001E07C07C00> 36 20 -2 0 40] 109 @dc cmr10.329 @sf [ 16 1 -3 -26 23] 22 @dc cmmi10.329 @sf [<383C00446300E2C080F1C080F1C04061C04000E02000E00000E00000E000007000007000007000 4070002038602038F01038F01034700C622003C1C0> 20 20 -2 0 26] 120 @dc cmmi8.300 @sf [<1F0060C04020C010C000C000C000C000FFC06020601030101C2007C0> 12 14 -2 0 16] 101 @dc cmmi10.329 @sf [<03E1E00613100E0F100C07080C07080E07080E03840E03800E03800E03800701C00701C00701C0 8381C04380E041C0E021C0E02180E01180700F0060> 22 20 -2 0 26] 117 @dc [<1F0031C060E06070E038E03CE01CE01EE01EE01E700F700F700F700F380F380F3C0E3A0E1D0C1C F01C001C000E000E000E000E0007000700070007003F800780> 16 32 -2 0 20] 98 @dc [<01FC0000078380000E00E0001C00700038003C0038001E0078000F007000070070000380F00003 C0F00001C0F00001E0F00000E0F00000F0F00000F0780000787800007878000078780000783C00 00383C0000381C0000381E0000380E00003807000038078000380380007001C0007000E0006000 3000E0001C01C0000707000001FC00> 29 33 -2 1 35] 79 @dc [<07E00C1818003000700070007000F000F000F0007FF07800780038003C001C000E00070001C000 7E> 15 20 -2 0 18] 15 @dc 1.000000 /cmbx10.329 @newfont cmbx10.329 @sf [ 30 31 -2 0 36] 80 @dc [ 18 20 -2 0 22] 114 @dc [<01FF0007FFC01F83F03E00F83E00F87C007C7C007CFC007EFC007EFC007EFC007EFC007EFC007E 7C007C7C007C3E00F83E00F81F83F007FFC001FF00> 23 20 -1 0 26] 111 @dc [<181F801C7FE01EC1F81F807C1F007C1F003E1F003E1F003F1F003F1F003F1F003F1F003F1F003F 1F003E1F003E1F007E1F807C1FE0F81F7FF01F1FC01F00001F00001F00001F00001F00001F0000 1F00001F00001F00001F0000FF0000FF0000> 24 32 -2 0 29] 98 @dc [ 11 32 -2 0 14] 108 @dc [<00FF8007FFE00F80701E00183E00187C00007C0000FC0000FC0000FC0000FFFFF8FFFFF8FC00F8 7C00F87C00F03E00F01E01E00F83C007FF8001FE00> 21 20 -1 0 24] 101 @dc [ 39 20 -3 0 46] 109 @dc [ 26 31 -2 0 31] 76 @dc [<01F003F807CC0F860F860F860F860F860F800F800F800F800F800F800F800F800F800F80FFFCFF FC3F800F800780038003800380018001800180> 15 29 -1 0 20] 116 @dc [<03F8FF07FCFF0F06F81F01F81F01F81F00F81F00F81F00F81F00F81F00F81F00F81F00F81F00F8 1F00F81F00F81F00F81F00F81F00F8FF07F8FF07F8> 24 20 -3 0 29] 117 @dc [<0FE07E3FF8FE7E0DE0FC05E0F803E0F803E0F803E07C03E03C03E01F03E007FBE0007FE00003E0 0C03E03F03E03F03E03F07C03F0F801FFF0007FC00> 23 20 -1 0 25] 97 @dc [ 11 33 -2 0 14] 105 @dc [ 24 20 -3 0 29] 110 @dc [ 31 31 -2 0 37] 66 @dc [<03F8FF0FFEFF1F07F83E01F87E00F87C00F87C00F8FC00F8FC00F8FC00F8FC00F8FC00F8FC00F8 7C00F87C00F87E00F83E01F81F83F80FFEF801F8F80000F80000F80000F80000F80000F80000F8 0000F80000F80000F80000F80007F80007F8> 24 32 -2 0 29] 100 @dc [ 16 20 -2 0 21] 115 @dc [<387CFEFEFE7C38000000000000387CFEFEFE7C38> 7 20 -4 0 15] 58 @dc cmsy10.329 @sf [<4020C030C030C030C030C030C030C030C030C030C030C030C030C030C030C030C030C030C030C0 30C030C030C030C030C030C030C030C030C030C030C030C030C030C030C030C030C030C030C030 C030C030C030C030C030C0304020> 12 46 -5 12 23] 107 @dc cmmi10.329 @sf [<6001E0E00310700310700708700708700708380384380700380700381E001FF8001F00001C8000 1C40000E20000E10000E0C600E02F00701F8060070> 22 20 -2 0 26] 20 @dc [ 23 29 1 9 23] 112 @dc cmmi8.300 @sf [ 23 23 -1 0 26] 65 @dc cmmi10.329 @sf [ 22 31 -1 0 20] 73 @dc cmti10.329 @sf [<07C3800C26401C1E20180E20180E201C0E201C07101C07001C07001C07000E03800E03800E0380 8703804701C04301C04381C02301C03300E00E00C0> 20 20 -4 0 24] 117 @dc [<1F0031C060E06070E038E03CE01CE01EE01EE01E700F700F700F700F380F380F3C0E3A0E1D0C1C F01C001C000E000E000E000E0007000700070007003F800780> 16 32 -5 0 21] 98 @dc cmmi10.329 @sf [<1800003800001C00001C00001C00001C00000E00000E00000E00000E0000070000070000070000 87000043830043878043C78023C3802321001E1E00> 17 20 -2 0 21] 114 @dc cmbx10.329 @sf [ 30 31 -2 0 34] 69 @dc [<3FFC003FFC0007C00007C00007C00007C00007C00007C00007C00007C00007C00007C00007C000 07C00007C00007C00007C00007C000FFFC00FFFC0007C00007C00007C00007C00007C00007C3C0 07C7E003C7E003E7E001F3E000FFC0001F80> 19 32 -1 0 16] 102 @dc [<01FC0007FF001F81C03F00C03E00607E00007C0000FC0000FC0000FC0000FC0000FC0000FC0000 7C03007C0FC03E0FC03E0FC01F0FC007FF8001FE00> 19 20 -2 0 23] 99 @dc cmsy8.300 @sf [<0F8007C010E01E6020303810400860088004C00C80078004800380048007000480078004C00C80 04401840082070301019E01C200F8007C0> 30 14 -2 0 35] 49 @dc 14 @bop1 cmsl10.329 @sf 60 -99 p m (The) 15 (Generalized) 17 (QR) 16 (Decomp) 1 (osition) ks cmr10.329 @sf 1037 r m (14) s 60 45 p m (and) 12 (also) 12 (assume) 12 (that) 11 (the) 12 (p) 1 (erturbated) 12 (system) 11 (has) 12 (unique) 13 (solution,) 13 (i.e.,) 13 (rank) ks 1529 45 p m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf 3 r m (+) s cmmi10.329 @sf 3 r m (E) 3 (;) 8 (B) ks cmr10.329 @sf 6 r m (+) s cmmi10.329 @sf 3 r m (F) s cmr10.329 @sf 6 r m (\)) 14 (=) ks cmmi10.329 @sf 60 102 p m (n) s cmr10.329 @sf m (,) 11 (and) 11 (rank) ks 284 102 p m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (+) s cmmi10.329 @sf m (E) s cmr10.329 @sf 3 r m (\)) 13 (=) ks cmmi10.329 @sf 13 r m (m) s cmr10.329 @sf m (.) 18 (The) 10 (solutions) 11 (are) 10 (denoted) 11 (as) 13 (\026) ks cmmi10.329 @sf 1120 102 p m (x) s cmmi8.300 @sf 1146 109 p m (e) s cmr10.329 @sf 1175 102 p m (and) 13 (\026) ks cmmi10.329 @sf 1258 102 p m (u) s cmmi8.300 @sf 1284 109 p m (e) s cmr10.329 @sf 1303 102 p m (.) 18 (Then) 11 (w) 0 (e) 9 (ha) 0 (v) -1 (e) 9 (the) 10 (follo) 0 (wing) ks 60 158 p m (b) 1 (ounds) 19 (on) 17 (the) 18 (relativ) 0 (e) 17 (error) 17 (in) 21 (\026) ks cmmi10.329 @sf 700 158 p m (x) s cmmi8.300 @sf 726 165 p m (e) s cmr10.329 @sf 762 158 p m (and) 21 (\026) ks cmmi10.329 @sf 853 158 p m (u) s cmmi8.300 @sf 879 165 p m (e) s cmr10.329 @sf 915 158 p m (due) 18 (to) 17 (the) 18 (p) 1 (erturbations) 18 (of) ks cmmi10.329 @sf 17 r m (b) s cmr10.329 @sf m (,) s cmmi10.329 @sf 18 r m (A) s cmr10.329 @sf 17 r m (and) s cmmi10.329 @sf 18 r m (B) s cmr10.329 @sf 2 r m (,) 19 (where) ks 60 214 p m (eac) 0 (h) 15 (asymptotic) 16 (b) 1 (ound) 17 (has) 15 (a) 16 (+) ks cmmi10.329 @sf m (O) s cmr10.329 @sf 1 r m (\() s cmmi10.329 @sf m (\017) s cmr8.300 @sf 766 199 p m (2) s cmr10.329 @sf 786 214 p m (\)) 16 (term) 15 (\(i.e.,) 16 (the) 16 (higher) 17 (order) 15 (of) 16 (the) 16 (p) 1 (erturbation) 17 (data) ks cmmi10.329 @sf 60 271 p m (E) s cmr10.329 @sf 3 r m (,) s cmmi10.329 @sf 14 r m (F) s cmr10.329 @sf 22 r m (etc\)) 15 (whic) 0 (h) 15 (is) 15 (not) 15 (written.) ks cmbx10.329 @sf 131 396 p m (Problem) s 14 r save [<0007FC0600003FFF8E0000FE01FE0003F000FE0007E0007E000FC0007E001F80007E003F00007E 003F00007E007F00007E007E00007E007E00007E00FE003FFFE0FE003FFFE0FE00000000FE0000 0000FE00000000FE00000000FE000000007E000006007E000006007F000006003F00000E003F00 000E001F80001E000FC0001E0007E0003E0003F000FE0000FE03DE00003FFF0E000007FC0200> 35 31 -3 0 41] 71 @pc restore 41 r m (L) s save [ 45 31 -2 0 50] 77 @pc restore 68 r m (P) 0 (erturbation) 17 (Bounds:) ks cmsy10.329 @sf 103 475 p m (k) s cmr10.329 @sf 3 r m (\026) s cmmi10.329 @sf 126 475 p m (x) s cmmi8.300 @sf 152 482 p m (e) s cmsy10.329 @sf 181 475 p m (\000) s cmmi10.329 @sf 10 r m (x) s cmmi8.300 @sf 252 482 p m (e) s cmsy10.329 @sf 270 475 p m (k) s 103 495 p 190 2 ru 153 537 p m (k) s cmmi10.329 @sf m (x) s cmmi8.300 @sf 202 544 p m (e) s cmsy10.329 @sf 220 537 p m (k) s 311 505 p save [ 26 36 -4 7 35] 20 @pc restore cmmi10.329 @sf 48 r m (\024) s cmmi8.300 @sf 385 512 p m (B) s cmr10.329 @sf 415 505 p m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) s 493 446 p save [<0000300000600000C0000180000300000700000E00000C0000180000380000300000700000E000 00C00001C0000180000380000380000300000700000600000E00000E00000C00001C00001C0000 1C0000180000380000380000380000380000700000700000700000700000700000700000700000 E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000 E00000E00000E00000E00000E00000E00000E00000E00000700000700000700000700000700000 7000007000003800003800003800003800001800001C00001C00001C00000C00000E00000E0000 06000007000003000003800003800001800001C00000C00000E000007000003000003800001800 000C00000E000007000003000001800000C0000060000030> 20 99 -9 97 31] 18 @pc restore cmsy10.329 @sf 528 475 p m (k) s cmmi10.329 @sf m (E) s cmsy10.329 @sf 3 r m (k) s 528 495 p 82 2 ru 529 537 p m (k) s cmmi10.329 @sf m (A) s cmsy10.329 @sf m (k) s cmr10.329 @sf 625 505 p m (+) s cmsy10.329 @sf 733 475 p m (k) s cmmi10.329 @sf m (e) s cmsy10.329 @sf m (k) s 675 495 p 183 2 ru 675 537 p m (k) s cmmi10.329 @sf m (A) s cmsy10.329 @sf m (k) 12 (k) ks cmmi10.329 @sf m (x) s cmmi8.300 @sf 816 544 p m (e) s cmsy10.329 @sf 834 537 p m (k) s 862 446 p save [ 20 99 -1 97 31] 19 @pc restore cmr10.329 @sf 903 505 p m (+) s cmmi10.329 @sf 10 r m (\024) s cmmi8.300 @sf 974 512 p m (B) s cmr10.329 @sf 1005 505 p m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) s 1083 446 p save [<0000300000600000C0000180000300000700000E00000C0000180000380000300000700000E000 00C00001C0000180000380000380000300000700000600000E00000E00000C00001C00001C0000 1C0000180000380000380000380000380000700000700000700000700000700000700000700000 E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000 E00000E00000E00000E00000E00000E00000E00000E00000700000700000700000700000700000 7000007000003800003800003800003800001800001C00001C00001C00000C00000E00000E0000 06000007000003000003800003800001800001C00000C00000E000007000003000003800001800 000C00000E000007000003000001800000C0000060000030> 20 99 -9 97 31] 18 @pc restore cmmi10.329 @sf 1112 505 p m (\024) s cmmi8.300 @sf 1138 512 p m (B) s cmr10.329 @sf 1169 505 p m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) s cmsy10.329 @sf 1244 475 p m (k) s cmmi10.329 @sf m (E) s cmsy10.329 @sf 3 r m (k) s 1244 495 p 82 2 ru 1245 537 p m (k) s cmmi10.329 @sf m (A) s cmsy10.329 @sf m (k) s cmr10.329 @sf 1340 505 p m (+) s cmsy10.329 @sf 1390 475 p m (k) s cmmi10.329 @sf m (F) s cmr8.300 @sf 1442 482 p m (1) s cmsy10.329 @sf 1462 475 p m (k) s 1390 495 p 95 2 ru 1396 537 p m (k) s cmmi10.329 @sf m (B) s cmsy10.329 @sf 2 r m (k) s 1490 446 p save [ 20 99 -1 97 31] 19 @pc restore cmsy10.329 @sf 1533 475 p m (k) s cmmi10.329 @sf m (B) s cmsy10.329 @sf 2 r m (k) s cmr8.300 @sf 1615 460 p m (2) s cmsy10.329 @sf 1647 475 p m (k) s cmmi10.329 @sf m (p) s cmsy10.329 @sf m (k) s 1533 495 p 183 2 ru 1533 537 p m (k) s cmmi10.329 @sf m (A) s cmsy10.329 @sf m (k) 12 (k) ks cmmi10.329 @sf m (x) s cmmi8.300 @sf 1674 544 p m (e) s cmsy10.329 @sf 1692 537 p m (k) s cmmi10.329 @sf 1721 505 p m (;) s cmr10.329 @sf 1779 505 p m (\(11\)) s 60 620 p m (and) s cmsy10.329 @sf 101 700 p m (k) s cmr10.329 @sf 3 r m (\026) s cmmi10.329 @sf 124 700 p m (u) s cmmi8.300 @sf 150 707 p m (e) s cmsy10.329 @sf 179 700 p m (\000) s cmmi10.329 @sf 10 r m (u) s cmmi8.300 @sf 250 707 p m (e) s cmsy10.329 @sf 269 700 p m (k) s 101 720 p 190 2 ru 164 761 p m (k) s cmmi10.329 @sf m (b) s cmsy10.329 @sf m (k) s 309 730 p save [ 26 36 -4 7 35] 20 @pc restore cmmi10.329 @sf 48 r m (\024) s cmmi8.300 @sf 383 737 p m (B) s cmr10.329 @sf 414 730 p m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) s cmsy10.329 @sf 489 700 p m (k) s cmmi10.329 @sf m (E) s cmsy10.329 @sf 3 r m (k) s 489 720 p 82 2 ru 490 761 p m (k) s cmmi10.329 @sf m (A) s cmsy10.329 @sf m (k) s 580 700 p m (k) s cmmi10.329 @sf m (B) s cmsy10.329 @sf 2 r m (k) 12 (k) ks cmmi10.329 @sf m (p) s cmsy10.329 @sf m (k) s 580 720 p 164 2 ru 629 761 p m (k) s cmmi10.329 @sf m (b) s cmsy10.329 @sf m (k) s cmr10.329 @sf 758 730 p m (+) s cmmi10.329 @sf 808 700 p m (\024) s cmr8.300 @sf 834 685 p m (2) s cmmi8.300 @sf 834 712 p m (A) s cmr10.329 @sf 863 700 p m (\() s cmmi10.329 @sf m (B) s cmr10.329 @sf 2 r m (\)) s 808 720 p 127 2 ru cmsy10.329 @sf 831 761 p m (k) s cmmi10.329 @sf m (B) s cmsy10.329 @sf 2 r m (k) s 948 671 p save [<0000300000600000C0000180000300000700000E00000C0000180000380000300000700000E000 00C00001C0000180000380000380000300000700000600000E00000E00000C00001C00001C0000 1C0000180000380000380000380000380000700000700000700000700000700000700000700000 E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000 E00000E00000E00000E00000E00000E00000E00000E00000700000700000700000700000700000 7000007000003800003800003800003800001800001C00001C00001C00000C00000E00000E0000 06000007000003000003800003800001800001C00000C00000E000007000003000003800001800 000C00000E000007000003000001800000C0000060000030> 20 99 -9 97 31] 18 @pc restore cmsy10.329 @sf 978 730 p m (k) s cmmi10.329 @sf m (E) s cmsy10.329 @sf 3 r m (k) s 1077 700 p m (k) s cmmi10.329 @sf m (x) s cmmi8.300 @sf 1126 707 p m (e) s cmsy10.329 @sf 1145 700 p m (k) s 1077 720 p 90 2 ru 1090 761 p m (k) s cmmi10.329 @sf m (b) s cmsy10.329 @sf m (k) s cmr10.329 @sf 1182 730 p m (+) s cmsy10.329 @sf 1233 700 p m (k) s cmmi10.329 @sf m (e) s cmsy10.329 @sf m (k) s 1233 720 p 67 2 ru 1234 761 p m (k) s cmmi10.329 @sf m (b) s cmsy10.329 @sf m (k) s cmr10.329 @sf 1314 730 p m (+) s cmsy10.329 @sf 11 r m (k) s cmmi10.329 @sf m (F) s cmr8.300 @sf 1412 737 p m (1) s cmsy10.329 @sf 1432 730 p m (k) s 1472 700 p m (k) s cmmi10.329 @sf m (p) s cmsy10.329 @sf m (k) s 1472 720 p 69 2 ru 1474 761 p m (k) s cmmi10.329 @sf m (b) s cmsy10.329 @sf m (k) s 1545 671 p save [ 20 99 -1 97 31] 19 @pc restore cmr10.329 @sf 1586 730 p m (+) s cmsy10.329 @sf 10 r m (k) s cmmi10.329 @sf m (F) s cmsy10.329 @sf 6 r m (k) s 1730 700 p m (k) s cmmi10.329 @sf m (p) s cmsy10.329 @sf m (k) s 1730 720 p 69 2 ru 1732 761 p m (k) s cmmi10.329 @sf m (b) s cmsy10.329 @sf m (k) s cmmi10.329 @sf 1803 730 p m (;) s cmr10.329 @sf 1779 811 p m (\(12\)) s 60 867 p m (where) s cmmi10.329 @sf 476 924 p m (\024) s cmmi8.300 @sf 502 931 p m (B) s cmr10.329 @sf 533 924 p m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) 12 (=) ks cmsy10.329 @sf 13 r m (k) s cmmi10.329 @sf m (A) s cmsy10.329 @sf m (k) 12 (k) ks cmmi10.329 @sf m (A) s cmr8.300 @sf 812 906 p m (+) s cmmi8.300 @sf 812 938 p m (I) 3 (B) ks cmsy10.329 @sf 860 924 p m (k) s cmmi10.329 @sf m (;) 70 (\024) ks cmmi8.300 @sf 992 931 p m (A) s cmr10.329 @sf 1021 924 p m (\() s cmmi10.329 @sf m (B) s cmr10.329 @sf 2 r m (\)) 12 (=) ks cmsy10.329 @sf 13 r m (k) s cmmi10.329 @sf m (B) s cmsy10.329 @sf 2 r m (k) 13 (k) ks cmr10.329 @sf m (\() s cmmi10.329 @sf save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore 36 r m (B) s cmr10.329 @sf 2 r m (\)) s cmr8.300 @sf 1379 906 p m (+) s cmsy10.329 @sf 1408 924 p m (k) s cmmi10.329 @sf m (;) s 60 1003 p save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmr10.329 @sf 48 r m (=) s cmmi10.329 @sf 13 r m (I) s cmsy10.329 @sf 14 r m (\000) s cmmi10.329 @sf 10 r m (AA) s cmr8.300 @sf 303 988 p m (+) s cmr10.329 @sf 333 1003 p m (,) s cmmi10.329 @sf 15 r m (A) s cmr8.300 @sf 395 985 p m (+) s cmmi8.300 @sf 395 1017 p m (I) 3 (B) ks cmr10.329 @sf 456 1003 p m (=) s cmmi10.329 @sf 13 r m (A) s cmr8.300 @sf 538 988 p m (+) s cmr10.329 @sf 567 1003 p m (\() s cmmi10.329 @sf m (I) s cmsy10.329 @sf 14 r m (\000) s cmmi10.329 @sf 10 r m (B) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore 36 r m (B) s cmr10.329 @sf 2 r m (\)) s cmr8.300 @sf 808 988 p m (+) s cmr10.329 @sf 838 1003 p m (\)) 15 (and) ks cmmi10.329 @sf 16 r m (p) s cmr10.329 @sf 12 r m (=) 13 (\() ks cmmi10.329 @sf save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore 36 r m (B) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore 36 r m (B) s cmr10.329 @sf 2 r m (\)) s cmr8.300 @sf 1241 988 p m (T) s cmr10.329 @sf 1269 1003 p m (\)) s cmr8.300 @sf 1287 988 p m (+) s cmmi10.329 @sf 1316 1003 p m (b) s cmr10.329 @sf m (,) s cmmi10.329 @sf 14 r m (F) s cmr8.300 @sf 1392 1010 p m (1) s cmr10.329 @sf 1425 1003 p m (=) s cmmi10.329 @sf 13 r m (B) 2 (F) ks cmr8.300 @sf 1544 988 p m (T) s cmr10.329 @sf 1583 1003 p m (+) s cmmi10.329 @sf 10 r m (F) s cmr8.300 @sf 1663 988 p m (T) s cmmi10.329 @sf 1691 1003 p m (B) s cmr10.329 @sf 2 r m (.) s 131 1068 p m (The) 15 (pro) 1 (of) 15 (is) 16 (going) 15 (to) 14 (b) 1 (e) 16 (presen) 0 (ted) 15 (later.) ks 131 1132 p m (The) 15 (b) 1 (ounds) 16 (are) 15 (quite) 16 (complicated.) 21 (If) 16 (w) 0 (e) 13 (note) 15 (that) ks cmsy10.329 @sf 742 1226 p m (k) s cmmi10.329 @sf m (B) s cmsy10.329 @sf 2 r m (k) s cmr8.300 @sf 824 1208 p m (2) s cmsy10.329 @sf 844 1226 p m (k) s cmmi10.329 @sf m (p) s cmsy10.329 @sf m (k) s 12 r save [ 26 36 -4 7 35] 20 @pc restore cmmi10.329 @sf 48 r m (\024) s cmr8.300 @sf 999 1208 p m (2) s cmmi8.300 @sf 999 1237 p m (A) s cmr10.329 @sf 1028 1226 p m (\() s cmmi10.329 @sf m (B) s cmr10.329 @sf 2 r m (\)) s cmsy10.329 @sf m (k) s cmmi10.329 @sf m (b) s cmsy10.329 @sf m (k) s cmmi10.329 @sf m (:) s cmr10.329 @sf 60 1319 p m (then) 15 (the) 14 (b) 1 (ounds) 15 (\(11\)) 13 (and) 15 (\(12\)) 13 (can) 14 (b) 1 (e) 15 (simpli\014e) 1 (d) 16 (a) 14 (little) 16 (bit.) 20 (W) -3 (e) 13 (see) 15 (that) 13 (the) 15 (sensitivities) 16 (of) ks 63 1376 p m (\026) s cmmi10.329 @sf 60 1376 p m (x) s cmmi8.300 @sf 86 1383 p m (e) s cmr10.329 @sf 119 1376 p m (and) 18 (\026) ks cmmi10.329 @sf 207 1376 p m (u) s cmmi8.300 @sf 233 1383 p m (e) s cmr10.329 @sf 266 1376 p m (dep) 1 (end) 16 (on) 14 (the) ks cmmi10.329 @sf 15 r m (\024) s cmmi8.300 @sf 589 1383 p m (B) s cmr10.329 @sf 620 1376 p m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) 14 (and) ks cmmi10.329 @sf 14 r m (\024) s cmmi8.300 @sf 817 1383 p m (A) s cmr10.329 @sf 846 1376 p m (\() s cmmi10.329 @sf m (B) s cmr10.329 @sf 2 r m (\).) 20 (F) -3 (or) 13 (this) 15 (reason,) ks cmmi10.329 @sf 14 r m (\024) s cmmi8.300 @sf 1300 1383 p m (B) s cmr10.329 @sf 1330 1376 p m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) 14 (and) ks cmmi10.329 @sf 15 r m (\024) s cmmi8.300 @sf 1528 1383 p m (A) s cmr10.329 @sf 1557 1376 p m (\() s cmmi10.329 @sf m (B) s cmr10.329 @sf 2 r m (\)) 14 (are) 15 (de\014ned) ks 60 1432 p m (as) 12 (the) ks cmti10.329 @sf 13 r m (c) -1 (ondition) 13 (numb) -1 (ers) ks cmr10.329 @sf 11 r m (of) 12 (Problem) 13 (GLM.) 12 (They) 13 (can) 13 (b) 1 (e) 14 (used) 13 (to) 12 (predict) 14 (the) 13 (e\013ects) 12 (of) 13 (errors) ks 60 1488 p m (in) 16 (the) 15 (regression) 16 (v) -2 (ariables) 15 (on) 15 (regression) 16 (co) 1 (e) ks save [<7FE3FE3FF007007007000700700700070070070007007007000700700700070070070007007007 000700700700070070070007007007000700700700070070070007007007000700700700070070 0700070070070007007007000700700700FFFFFFFF000700700000070070000007007000000700 700000070070000007007000000700F00F000300F00F000380F80F0001C07C060000F04F040000 1F81F800> 36 32 0 0 38] 14 @pc restore 38 r m (cien) 0 (ts.) ks 131 1553 p m (As) 12 (sp) 1 (ecial) 15 (case,) 12 (w) 0 (e) 12 (note) 12 (that) 12 (if) ks cmmi10.329 @sf 13 r m (B) s cmr10.329 @sf 16 r m (=) s cmmi10.329 @sf 13 r m (I) s cmr10.329 @sf 4 r m (,) 12 (then) 13 (the) 13 (problem) 13 (GLM) 13 (is) 13 (reduced) 14 (to) 12 (the) 12 (classical) ks 60 1610 p m (linear) 12 (regression) 11 (problem.) ks cmmi10.329 @sf 19 r m (u) s cmmi8.300 @sf 607 1617 p m (e) s cmr10.329 @sf 636 1610 p m (is) 12 (just) 10 (the) 11 (residual) 13 (v) 0 (ector,) ks cmmi10.329 @sf 9 r m (u) s cmmi8.300 @sf 1174 1617 p m (e) s cmr10.329 @sf 1205 1610 p m (=) s cmmi10.329 @sf 13 r m (p) s cmr10.329 @sf 13 r m (=) s cmmi10.329 @sf 13 r m (r) s cmmi8.300 @sf 1358 1617 p m (e) s cmr10.329 @sf 1388 1610 p m (=) s cmmi10.329 @sf 13 r m (b) s cmsy10.329 @sf 1 r m (\000) s cmmi10.329 @sf 1 r m (Ax) s cmmi8.300 @sf 1553 1617 p m (e) s cmr10.329 @sf 1585 1610 p m (=) 13 (\() ks cmmi10.329 @sf m (I) s cmsy10.329 @sf 5 r m (\000) s cmmi10.329 @sf 1 r m (AA) s cmr8.300 @sf 1780 1595 p m (+) s cmr10.329 @sf 1810 1610 p m (\)) s cmmi10.329 @sf m (b) s cmr10.329 @sf m (,) s 63 1666 p m (\026) s cmmi10.329 @sf 60 1666 p m (u) s cmr10.329 @sf 99 1666 p m (=) 15 (\026) ks cmmi10.329 @sf 147 1666 p m (r) s cmr10.329 @sf 181 1666 p m (=) 13 (\() ks cmmi10.329 @sf m (b) s cmr10.329 @sf 9 r m (+) s cmmi10.329 @sf 11 r m (e) s cmr10.329 @sf m (\)) s cmsy10.329 @sf 10 r m (\000) s cmr10.329 @sf 10 r m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf 10 r m (+) s cmmi10.329 @sf 10 r m (E) s cmr10.329 @sf 3 r m (\)) 3 (\026) ks cmmi10.329 @sf 578 1666 p m (x) s cmr10.329 @sf 603 1666 p m (,) s cmmi10.329 @sf 15 r m (F) s cmr10.329 @sf 19 r m (=) 13 (0,) 15 (and) ks cmmi10.329 @sf 529 1759 p m (\024) s cmmi8.300 @sf 555 1766 p m (B) s cmr10.329 @sf 585 1759 p m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) 12 (=) ks cmmi10.329 @sf 13 r m (\024) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) 12 (=) ks cmsy10.329 @sf 13 r m (k) s cmmi10.329 @sf m (A) s cmsy10.329 @sf m (k) 13 (k) ks cmmi10.329 @sf m (A) s cmr8.300 @sf 1021 1741 p m (+) s cmsy10.329 @sf 1050 1759 p m (k) s cmmi10.329 @sf m (;) 83 (\024) ks cmmi8.300 @sf 1195 1766 p m (A) s cmr10.329 @sf 1223 1759 p m (\() s cmmi10.329 @sf m (B) s cmr10.329 @sf 2 r m (\)) 13 (=) 13 (1) ks cmmi10.329 @sf m (:) s cmr10.329 @sf 60 1853 p m (Hence) 16 (w) 0 (e) 14 (ha) 0 (v) -1 (e) ks cmsy10.329 @sf 273 1929 p m (k) s cmr10.329 @sf 3 r m (\026) s cmmi10.329 @sf 296 1929 p m (x) s cmmi8.300 @sf 322 1936 p m (e) s cmsy10.329 @sf 351 1929 p m (\000) s cmmi10.329 @sf 10 r m (x) s cmmi8.300 @sf 422 1936 p m (e) s cmsy10.329 @sf 440 1929 p m (k) s 273 1949 p 190 2 ru 332 1990 p m (k) s cmmi10.329 @sf m (x) s cmsy10.329 @sf m (k) s 481 1959 p save [ 26 36 -4 7 35] 20 @pc restore cmmi10.329 @sf 48 r m (\024) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) s 633 1899 p save [<0000300000600000C0000180000300000700000E00000C0000180000380000300000700000E000 00C00001C0000180000380000380000300000700000600000E00000E00000C00001C00001C0000 1C0000180000380000380000380000380000700000700000700000700000700000700000700000 E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000 E00000E00000E00000E00000E00000E00000E00000E00000700000700000700000700000700000 7000007000003800003800003800003800001800001C00001C00001C00000C00000E00000E0000 06000007000003000003800003800001800001C00000C00000E000007000003000003800001800 000C00000E000007000003000001800000C0000060000030> 20 99 -9 97 31] 18 @pc restore cmsy10.329 @sf 667 1929 p m (k) s cmmi10.329 @sf m (E) s cmsy10.329 @sf 3 r m (k) s 667 1949 p 82 2 ru 668 1990 p m (k) s cmmi10.329 @sf m (A) s cmsy10.329 @sf m (k) s cmr10.329 @sf 764 1959 p m (+) s cmsy10.329 @sf 872 1929 p m (k) s cmmi10.329 @sf m (e) s cmsy10.329 @sf m (k) s 815 1949 p 183 2 ru 815 1990 p m (k) s cmmi10.329 @sf m (A) s cmsy10.329 @sf m (k) 12 (k) ks cmmi10.329 @sf m (x) s cmmi8.300 @sf 956 1997 p m (e) s cmsy10.329 @sf 974 1990 p m (k) s 1002 1899 p save [ 20 99 -1 97 31] 19 @pc restore cmr10.329 @sf 1042 1959 p m (+) s cmmi10.329 @sf 11 r m (\024) s cmr8.300 @sf 1114 1941 p m (2) s cmr10.329 @sf 1134 1959 p m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) s cmsy10.329 @sf 1209 1929 p m (k) s cmmi10.329 @sf m (E) s cmsy10.329 @sf 3 r m (k) s 1209 1949 p 82 2 ru 1210 1990 p m (k) s cmmi10.329 @sf m (A) s cmsy10.329 @sf m (k) s 1348 1929 p m (k) s cmmi10.329 @sf m (r) s cmmi8.300 @sf 1392 1936 p m (e) s cmsy10.329 @sf 1410 1929 p m (k) s 1300 1949 p 183 2 ru 1300 1990 p m (k) s cmmi10.329 @sf m (A) s cmsy10.329 @sf m (k) 12 (k) ks cmmi10.329 @sf m (x) s cmmi8.300 @sf 1441 1997 p m (e) s cmsy10.329 @sf 1459 1990 p m (k) s cmr10.329 @sf 1497 1959 p m (+) s cmmi10.329 @sf 10 r m (O) s cmr10.329 @sf 1 r m (\() s cmmi10.329 @sf m (\017) s cmr8.300 @sf 1614 1941 p m (2) s cmr10.329 @sf 1634 1959 p m (\)) s 60 2074 p m (and) s cmsy10.329 @sf 426 2113 p m (k) s cmr10.329 @sf 2 r m (\026) s cmmi10.329 @sf 449 2113 p m (r) s cmmi8.300 @sf 470 2120 p m (e) s cmsy10.329 @sf 498 2113 p m (\000) s cmmi10.329 @sf 10 r m (r) s cmmi8.300 @sf 564 2120 p m (e) s cmsy10.329 @sf 582 2113 p m (k) s 426 2133 p 179 2 ru 483 2174 p m (k) s cmmi10.329 @sf m (b) s cmsy10.329 @sf m (k) s 623 2143 p save [ 26 36 -4 7 35] 20 @pc restore cmmi10.329 @sf 48 r m (\024) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) s cmsy10.329 @sf 772 2113 p m (k) s cmmi10.329 @sf m (E) s cmsy10.329 @sf 3 r m (k) s 772 2133 p 82 2 ru 773 2174 p m (k) s cmmi10.329 @sf m (A) s cmsy10.329 @sf m (k) s 863 2113 p m (k) s cmmi10.329 @sf m (r) s cmmi8.300 @sf 907 2120 p m (e) s cmsy10.329 @sf 924 2113 p m (k) s 863 2133 p 85 2 ru 872 2174 p m (k) s cmmi10.329 @sf m (b) s cmsy10.329 @sf m (k) s cmr10.329 @sf 962 2143 p m (+) s cmsy10.329 @sf 11 r m (k) s cmmi10.329 @sf m (E) s cmsy10.329 @sf 3 r m (k) s 1107 2113 p m (k) s cmmi10.329 @sf m (x) s cmmi8.300 @sf 1156 2120 p m (e) s cmsy10.329 @sf 1174 2113 p m (k) s 1107 2133 p 90 2 ru 1119 2174 p m (k) s cmmi10.329 @sf m (b) s cmsy10.329 @sf m (k) s cmr10.329 @sf 1212 2143 p m (+) s cmsy10.329 @sf 1262 2113 p m (k) s cmmi10.329 @sf m (e) s cmsy10.329 @sf m (k) s 1262 2133 p 67 2 ru 1263 2174 p m (k) s cmmi10.329 @sf m (b) s cmsy10.329 @sf m (k) s cmr10.329 @sf 1344 2143 p m (+) s cmmi10.329 @sf 10 r m (O) s cmr10.329 @sf 1 r m (\() s cmmi10.329 @sf m (\017) s cmr8.300 @sf 1461 2125 p m (2) s cmr10.329 @sf 1481 2143 p m (\)) s 60 2244 p m (These) 21 (are) 21 (the) 21 (w) 0 (ell-kno) 0 (wn) 20 (p) 1 (erturbation) 21 (results) 22 (for) 20 (the) 21 (solution) 22 (and) 21 (residual) 22 (of) 21 (ordinary) ks 60 2300 p m (linear) 16 (least) 16 (regression) 15 (problem) 16 ([) 0 (11) ks 738 2300 p m (,) 15 (4) ks 789 2300 p m (].) s cmbx10.329 @sf 131 2365 p m (Estimation) 12 (of) 13 (condition) 15 (n) 0 (um) -4 (b) 1 (ers:) ks cmr10.329 @sf 15 r m (Concerning) 12 (ab) 1 (out) 11 (the) 11 (estimating) 12 (of) 10 (the) 12 (condition) ks 60 2421 p m (n) 0 (um) 0 (b) 1 (ers) ks cmmi10.329 @sf 13 r m (\024) s cmmi8.300 @sf 269 2428 p m (B) s cmr10.329 @sf 300 2421 p m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) 14 (and) ks cmmi10.329 @sf 15 r m (\024) s cmmi8.300 @sf 498 2428 p m (A) s cmr10.329 @sf 527 2421 p m (\() s cmmi10.329 @sf m (B) s cmr10.329 @sf 2 r m (\)) 15 (of) 14 (the) 15 (Problem) 16 (GLM,) 14 (w) 0 (e) 14 (still) 16 (can) 15 (use) 15 (the) 16 (Hager) 14 (and) 15 (Higham's) ks 60 2478 p m (metho) 1 (d) 14 (without) 13 (forming) 13 (exp) 1 (ensiv) 0 (e) ks cmmi10.329 @sf 14 r m (A) s cmr8.300 @sf 794 2463 p m (+) s cmr10.329 @sf 837 2478 p m (or) 13 (\() ks cmmi10.329 @sf save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore 36 r m (B) s cmr10.329 @sf 2 r m (\)) s cmr8.300 @sf 999 2463 p m (+) s cmr10.329 @sf 1028 2478 p m (.) 19 (T) -3 (o) 13 (use) 13 (their) 14 (metho) 1 (d,) 14 (the) 13 (required) 15 (v) 0 (ector) ks 60 2534 p m (norms) s cmsy10.329 @sf 15 r m (k) s cmmi10.329 @sf save [ 37 31 -2 0 39] 75 @pc restore 42 r m (z) s cmsy10.329 @sf 2 r m (k) s cmsy8.300 @sf 308 2541 p m (1) s cmr10.329 @sf 360 2534 p m (can) 16 (b) 1 (e) 16 (computed) 16 (b) 0 (y) 14 (GQR) 16 (factorization) 16 (of) ks cmmi10.329 @sf 15 r m (A) s cmr10.329 @sf 15 r m (and) s cmmi10.329 @sf 16 r m (B) s cmr10.329 @sf 2 r m (,) 16 (where) ks cmmi10.329 @sf 15 r save [ 37 31 -2 0 39] 75 @pc restore cmr10.329 @sf 55 r m (=) 14 (\() ks cmmi10.329 @sf save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore 36 r m (B) s cmr10.329 @sf 2 r m (\)) s cmr8.300 @sf 1762 2519 p m (+) s cmr10.329 @sf 1791 2534 p m (,) 15 (or) ks cmmi10.329 @sf 60 2591 p save [ 37 31 -2 0 39] 75 @pc restore cmr10.329 @sf 56 r m (=) s cmmi10.329 @sf 15 r m (A) s cmr8.300 @sf 200 2573 p m (+) s cmmi8.300 @sf 200 2604 p m (I) 3 (B) ks cmr10.329 @sf 265 2591 p m (and) s cmmi10.329 @sf 16 r m (z) s cmsy10.329 @sf 17 r save [ 26 36 -4 7 35] 21 @pc restore cmr10.329 @sf 50 r m (0) 16 (is) 17 (a) 16 (v) 0 (ector) 14 (that) 16 (is) 17 (readily) 17 (computed.) 24 (After) 16 (tedious) 17 (computations,) 16 (w) 0 (e) ks 60 2647 p m (ha) 0 (v) -1 (e) ks 744 2704 p m (\() s cmmi10.329 @sf save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore 36 r m (B) s cmr10.329 @sf 2 r m (\)) s cmr8.300 @sf 852 2686 p m (+) s cmmi10.329 @sf 882 2704 p m (z) s cmr10.329 @sf 14 r m (=) s cmmi10.329 @sf 13 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr8.300 @sf 992 2711 p m (2) s cmmi10.329 @sf 1012 2704 p m (S) s cmsy8.300 @sf 1043 2686 p m (\000) s cmr8.300 @sf m (1) s 1040 2716 p m (22) s cmmi10.329 @sf 1089 2704 p m (Q) s cmr8.300 @sf 1125 2686 p m (T) s 1125 2715 p m (2) s cmmi10.329 @sf 1153 2704 p m (z) s @eop 13 @bop0 cmsy10.329 @sf [<400004C0000C6000183000301800600C00C006018003030001860000CC00007800003000003000 00780000CC000186000303000601800C00C0180060300030600018C0000C400004> 22 24 -6 1 35] 2 @dc cmmi10.329 @sf [<0FFE0000E00000E0000070000070000070000070000038000038000F380030B800705C00703C00 F01C00F01C00F00E00F00E00F00E00F00E007807007807007807003807003C03801C03800E0380 0705800388C000F040> 18 29 -2 9 20] 113 @dc 1.000000 /cmex10.300 @newfont cmex10.300 @sf [ 8 74 -10 72 20] 104 @dc [ 8 74 -1 72 20] 105 @dc cmmi10.329 @sf [<0FC01838300470027001F000F000F000F000F0007800780078003C041C0E1E0F0E0F070101C200 7C> 16 20 -2 0 20] 99 @dc cmsy10.329 @sf [ 28 20 -3 -1 35] 17 @dc cmmi10.329 @sf [<01E0000618000E04000E04000C02000E01000E01000E00800E00800E0080070040070040070040 83804043806041C0E021C1E02183E01183C00F0180> 19 20 -2 0 22] 118 @dc cmmi8.300 @sf [<1C0032003200310031001800180018000C008C004600460024001C000000000000000000000000 00030003800300> 9 23 -1 0 12] 105 @dc cmmi10.329 @sf [<0E00190038803840384038401C201C001C000E000E00070007008700438043804380238013000E 00000000000000000000000000000000C001E001E000E0> 11 31 -2 0 16] 105 @dc cmr10.329 @sf [<381C7C3EFC7EFC7EB85C804080408040402040202010201010080804> 15 14 -5 -18 23] 92 @dc [<402020101008100808040804040204020402743AFC7EFC7EF87C7038> 15 14 -2 -18 23] 34 @dc [<40202010101008080878F8F8F0700000000000000000000070F8F8F870> 5 29 -4 9 13] 59 @dc cmbx10.329 @sf [<001C0000001C0000003E0000003E0000007F0000007F000000FF800000F9800001F9C00001F0C0 0001F0C00003E0600003E0600007C0300007C030000F8018000F8018001F001C00FFE07F80FFE0 7F80> 25 20 -1 0 28] 118 @dc cmr8.300 @sf [ 13 1 -2 -18 18] 22 @dc cmmi8.300 @sf [<78F000C50800E70400C3020003020003000001800001800001800041800020C30020C38011A180 0F1F00> 17 14 -1 0 20] 120 @dc [<40402020101070F0F060> 4 10 -3 6 10] 59 @dc [<078E000C59001838801818801818801818000C0C000C0C000C0C00860C00460600460600260600 1C0200> 17 14 -1 0 20] 117 @dc 13 @bop1 cmsl10.329 @sf 60 -99 p m (The) 15 (Generalized) 17 (QR) 16 (Decomp) 1 (osition) ks cmr10.329 @sf 1037 r m (13) s 131 45 p m (By) 14 (the) 14 (GQR) 15 (factorization) 14 (with) 15 (piv) 0 (oting) 13 (of) ks cmmi10.329 @sf 14 r m (A) s cmr10.329 @sf 15 r m (and) s cmmi10.329 @sf 14 r m (B) s cmr10.329 @sf 2 r m (,) 15 (under) 15 (the) 14 (uniqueness) 16 (assumption,) ks 60 102 p m (w) 0 (e) 14 (ha) 0 (v) -1 (e) 14 (orthogonal) 14 (matrices) ks cmmi10.329 @sf 15 r m (Q) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (n) s cmsy10.329 @sf 10 r m (\002) s cmmi10.329 @sf 11 r m (n) s cmr10.329 @sf m (\),) s cmmi10.329 @sf 15 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr10.329 @sf 36 r m (\() s cmmi10.329 @sf m (p) s cmsy10.329 @sf 10 r m (\002) s cmmi10.329 @sf 11 r m (p) s cmr10.329 @sf m (\),) 14 (and) ks cmmi10.329 @sf 15 r m (m) s cmr10.329 @sf 15 r m (b) 0 (y) ks cmmi10.329 @sf 15 r m (m) s cmr10.329 @sf 15 r m (p) 1 (erm) 0 (utation) 14 (matrix) ks cmmi10.329 @sf 15 r m (P) s cmr10.329 @sf 22 r m (suc) 0 (h) ks 60 158 p m (that) s cmmi10.329 @sf 228 283 p m (Q) s cmr8.300 @sf 264 267 p m (T) s cmmi10.329 @sf 291 283 p m (AP) s cmr10.329 @sf 20 r m (=) s cmex10.300 @sf 450 209 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 495 255 p m (R) s cmr8.300 @sf 530 262 p m (11) s cmmi10.329 @sf 609 255 p m (R) s cmr8.300 @sf 644 262 p m (12) s cmr10.329 @sf 520 310 p m (0) s 633 310 p m (0) s cmex10.300 @sf 701 209 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 735 255 p m (q) s 735 310 p m (n) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 11 r m (q) s 498 372 p m (q) s 561 372 p m (m) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 11 r m (q) s 881 310 p m (;) s 960 283 p m (Q) s cmr8.300 @sf 996 267 p m (T) s cmmi10.329 @sf 1023 283 p m (B) s 2 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr10.329 @sf 50 r m (=) s cmex10.300 @sf 1241 209 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 1286 255 p m (S) s cmr8.300 @sf 1314 262 p m (11) s cmmi10.329 @sf 1393 255 p m (S) s cmr8.300 @sf 1421 262 p m (12) s cmr10.329 @sf 1307 310 p m (0) s cmmi10.329 @sf 1393 310 p m (S) s cmr8.300 @sf 1421 317 p m (22) s cmex10.300 @sf 1479 209 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 1567 255 p m (q) s 1567 310 p m (n) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (q) s 1207 372 p m (p) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 11 r m (n) s cmr10.329 @sf 10 r m (+) s cmmi10.329 @sf 10 r m (q) s 1432 372 p m (n) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 11 r m (q) s cmr10.329 @sf 60 470 p m (where) s cmmi10.329 @sf 14 r m (q) s cmr10.329 @sf 16 r m (b) 0 (y) ks cmmi10.329 @sf 13 r m (q) s cmr10.329 @sf 16 r m (matrix) s cmmi10.329 @sf 14 r m (R) s cmr8.300 @sf 506 477 p m (11) s cmr10.329 @sf 543 470 p m (,) s cmmi10.329 @sf 14 r m (n) s cmsy10.329 @sf 8 r m (\000) s cmmi10.329 @sf 8 r m (q) s cmr10.329 @sf 16 r m (b) 0 (y) ks cmmi10.329 @sf 13 r m (n) s cmsy10.329 @sf 8 r m (\000) s cmmi10.329 @sf 8 r m (q) s cmr10.329 @sf 16 r m (matrix) s cmmi10.329 @sf 14 r m (S) s cmr8.300 @sf 1035 477 p m (22) s cmr10.329 @sf 1086 470 p m (are) 14 (nonsingular) 15 (upp) 1 (er) 15 (triangular.) 20 (If) 14 (w) 0 (e) ks 60 527 p m (partition) s cmmi10.329 @sf 405 588 p m (Q) s cmr10.329 @sf 13 r m (=) s cmex10.300 @sf 502 541 p m (h) s cmmi10.329 @sf 542 588 p m (Q) s cmr8.300 @sf 578 595 p m (1) s cmmi10.329 @sf 639 588 p m (Q) s cmr8.300 @sf 675 595 p m (2) s cmex10.300 @sf 716 541 p m (i) s cmmi10.329 @sf 743 588 p m (;) s 45 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr10.329 @sf 49 r m (=) s cmex10.300 @sf 898 541 p m (h) s cmmi10.329 @sf 938 588 p save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr8.300 @sf 965 595 p m (1) s cmmi10.329 @sf 1026 588 p save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr8.300 @sf 1053 595 p m (2) s cmex10.300 @sf 1093 541 p m (i) s cmmi10.329 @sf 1120 588 p m (;) 45 (P) ks cmr10.329 @sf 20 r m (=) s cmex10.300 @sf 1275 541 p m (h) s cmmi10.329 @sf 1315 588 p m (P) s cmr8.300 @sf 1344 595 p m (1) s cmmi10.329 @sf 1405 588 p m (P) s cmr8.300 @sf 1434 595 p m (2) s cmex10.300 @sf 1475 541 p m (i) s cmmi10.329 @sf 1502 588 p m (;) s cmr10.329 @sf 60 677 p m (where) s cmmi10.329 @sf 15 r m (Q) s cmr8.300 @sf 227 684 p m (1) s cmr10.329 @sf 262 677 p m (has) s cmmi10.329 @sf 15 r m (q) s cmr10.329 @sf 17 r m (columns,) s cmmi10.329 @sf 16 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr8.300 @sf 597 684 p m (2) s cmr10.329 @sf 631 677 p m (has) s cmmi10.329 @sf 15 r m (n) s cmsy10.329 @sf 11 r m (\000) s cmmi10.329 @sf 10 r m (q) s cmr10.329 @sf 17 r m (columns,) s cmmi10.329 @sf 16 r m (P) s cmr8.300 @sf 1051 684 p m (1) s cmr10.329 @sf 1086 677 p m (has) s cmmi10.329 @sf 15 r m (q) s cmr10.329 @sf 17 r m (columns,) 16 (and) 15 (set) ks cmmi10.329 @sf 351 809 p m (c) s cmr10.329 @sf 13 r m (=) s cmmi10.329 @sf 13 r m (Q) s cmr8.300 @sf 468 791 p m (T) s cmmi10.329 @sf 495 809 p m (b) s cmsy10.329 @sf 12 r m (\021) s cmex10.300 @sf 575 737 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 620 782 p m (c) s cmr8.300 @sf 640 789 p m (1) s cmmi10.329 @sf 620 838 p m (c) s cmr8.300 @sf 640 845 p m (2) s cmex10.300 @sf 680 737 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 712 809 p m (;) 45 (v) ks cmr10.329 @sf 14 r m (=) s cmmi10.329 @sf 13 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr8.300 @sf 891 791 p m (T) s cmmi10.329 @sf 919 809 p m (u) s cmsy10.329 @sf 12 r m (\021) s cmex10.300 @sf 1005 737 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 1050 782 p m (v) s cmr8.300 @sf 1072 789 p m (1) s cmmi10.329 @sf 1050 838 p m (v) s cmr8.300 @sf 1072 845 p m (2) s cmex10.300 @sf 1113 737 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 1144 809 p m (;) s 46 r save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr10.329 @sf 36 r m (=) s cmmi10.329 @sf 13 r m (P) s cmr8.300 @sf 1322 791 p m (T) s cmmi10.329 @sf 1350 809 p m (x) s cmsy10.329 @sf 13 r m (\021) s cmex10.300 @sf 1437 737 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 1482 782 p save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 1504 789 p m (1) s cmmi10.329 @sf 1482 838 p save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 1504 845 p m (2) s cmex10.300 @sf 1544 737 p save [ 12 124 0 122 24] 35 @pc restore cmr10.329 @sf 60 949 p m (i.e.,) s cmmi10.329 @sf 15 r m (c) s cmmi8.300 @sf 166 956 p m (i) s cmr10.329 @sf 192 949 p m (=) s cmmi10.329 @sf 13 r m (Q) s cmr8.300 @sf 276 934 p m (T) s cmmi8.300 @sf 276 961 p m (i) s cmmi10.329 @sf 304 949 p m (b) s cmr10.329 @sf m (,) s cmmi10.329 @sf 14 r m (v) s cmmi8.300 @sf 373 956 p m (i) s cmr10.329 @sf 400 949 p m (=) s cmmi10.329 @sf 13 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr8.300 @sf 484 934 p m (T) s cmmi8.300 @sf 475 961 p m (i) s cmmi10.329 @sf 512 949 p m (u) s cmr10.329 @sf m (,) s cmmi10.329 @sf 15 r save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmmi8.300 @sf 588 956 p m (i) s cmr10.329 @sf 615 949 p m (=) s cmmi10.329 @sf 13 r m (P) s cmr8.300 @sf 698 934 p m (T) s cmmi8.300 @sf 692 961 p m (i) s cmmi10.329 @sf 726 949 p m (x) s cmr10.329 @sf m (,) s cmmi10.329 @sf 14 r m (i) s cmr10.329 @sf 13 r m (=) 13 (1) ks cmmi10.329 @sf m (;) s cmr10.329 @sf 8 r m (2,) 13 (then) 16 (the) 15 (problem) 16 (GLM) 15 (is) 15 (transformed) 15 (to) ks cmex10.300 @sf 423 1013 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 468 1058 p m (c) s cmr8.300 @sf 488 1065 p m (1) s cmmi10.329 @sf 468 1113 p m (c) s cmr8.300 @sf 488 1120 p m (2) s cmex10.300 @sf 528 1013 p save [ 12 124 0 122 24] 35 @pc restore cmr10.329 @sf 565 1085 p m (=) s cmex10.300 @sf 613 1013 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 658 1058 p m (R) s cmr8.300 @sf 693 1065 p m (11) s cmmi10.329 @sf 771 1058 p m (R) s cmr8.300 @sf 806 1065 p m (12) s cmr10.329 @sf 682 1113 p m (0) s 796 1113 p m (0) s cmex10.300 @sf 864 1013 p save [ 12 124 0 122 24] 35 @pc restore 896 1013 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 941 1058 p save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 963 1065 p m (1) s cmmi10.329 @sf 941 1113 p save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 963 1120 p m (2) s cmex10.300 @sf 1003 1013 p save [ 12 124 0 122 24] 35 @pc restore cmr10.329 @sf 1038 1085 p m (+) s cmex10.300 @sf 1083 1013 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 1128 1058 p m (S) s cmr8.300 @sf 1156 1065 p m (11) s cmmi10.329 @sf 1235 1058 p m (S) s cmr8.300 @sf 1263 1065 p m (12) s cmr10.329 @sf 1149 1113 p m (0) s cmmi10.329 @sf 1235 1113 p m (S) s cmr8.300 @sf 1263 1120 p m (22) s cmex10.300 @sf 1321 1013 p save [ 12 124 0 122 24] 35 @pc restore 1353 1013 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 1398 1058 p m (v) s cmr8.300 @sf 1420 1065 p m (1) s cmmi10.329 @sf 1398 1113 p m (v) s cmr8.300 @sf 1420 1120 p m (2) s cmex10.300 @sf 1460 1013 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 1492 1085 p m (:) s cmr10.329 @sf 1779 1085 p m (\(10\)) s 60 1217 p m (Hence) s cmmi10.329 @sf 16 r m (v) s cmr8.300 @sf 217 1224 p m (2) s cmr10.329 @sf 252 1217 p m (can) 15 (b) 1 (e) 16 (determined) 17 (from) 14 (the) 15 (\\b) 1 (ottom") 14 (equation) 16 (b) 0 (y) 14 (solving) 16 (a) 15 (triangular) 15 (system:) ks cmmi10.329 @sf 844 1319 p m (v) s cmr8.300 @sf 866 1326 p m (2) s cmr10.329 @sf 898 1319 p m (=) s cmmi10.329 @sf 13 r m (S) s cmsy8.300 @sf 977 1301 p m (\000) s cmr8.300 @sf m (1) s 974 1332 p m (22) s cmmi10.329 @sf 1024 1319 p m (c) s cmr8.300 @sf 1044 1326 p m (2) s cmmi10.329 @sf 1063 1319 p m (:) s cmr10.329 @sf 60 1421 p m (Then) 16 (from) 14 (the) 15 (\\top") 15 (equation,) 15 (w) 0 (e) 14 (ha) 0 (v) -1 (e) ks cmmi10.329 @sf 599 1523 p m (c) s cmr8.300 @sf 619 1530 p m (1) s cmr10.329 @sf 651 1523 p m (=) s cmmi10.329 @sf 13 r m (R) s cmr8.300 @sf 734 1530 p m (11) s cmmi10.329 @sf 771 1523 p save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 793 1530 p m (1) s cmr10.329 @sf 823 1523 p m (+) s cmmi10.329 @sf 11 r m (R) s cmr8.300 @sf 904 1530 p m (12) s cmmi10.329 @sf 941 1523 p save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 963 1530 p m (2) s cmr10.329 @sf 993 1523 p m (+) s cmmi10.329 @sf 10 r m (S) s cmr8.300 @sf 1066 1530 p m (11) s cmmi10.329 @sf 1104 1523 p m (v) s cmr8.300 @sf 1126 1530 p m (1) s cmr10.329 @sf 1155 1523 p m (+) s cmmi10.329 @sf 11 r m (S) s cmr8.300 @sf 1229 1530 p m (12) s cmmi10.329 @sf 1266 1523 p m (v) s cmr8.300 @sf 1288 1530 p m (2) s cmmi10.329 @sf 1308 1523 p m (:) s cmr10.329 @sf 60 1626 p m (It) 15 (is) 16 (ob) 0 (vious) 14 (that) 15 (the) 15 (rest) 15 (of) 15 (solutions) 16 (are) 14 (giv) 0 (en) 15 (b) 0 (y) ks cmmi10.329 @sf 522 1728 p m (v) s cmr8.300 @sf 544 1735 p m (1) s cmr10.329 @sf 576 1728 p m (=) 13 (0) ks cmmi10.329 @sf m (;) s 83 r save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 765 1735 p m (2) s cmr10.329 @sf 797 1728 p m (=) 13 (0) ks cmmi10.329 @sf m (;) s 83 r save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 986 1735 p m (1) s cmr10.329 @sf 1019 1728 p m (=) s cmmi10.329 @sf 12 r m (R) s cmsy8.300 @sf 1101 1710 p m (\000) s cmr8.300 @sf m (1) s 1101 1740 p m (11) s cmr10.329 @sf 1149 1728 p m (\() s cmmi10.329 @sf m (c) s cmr8.300 @sf 1187 1735 p m (1) s cmsy10.329 @sf 1216 1728 p m (\000) s cmmi10.329 @sf 10 r m (S) s cmr8.300 @sf 1289 1735 p m (12) s cmmi10.329 @sf 1326 1728 p m (v) s cmr8.300 @sf 1348 1735 p m (2) s cmr10.329 @sf 1368 1728 p m (\)) s cmmi10.329 @sf m (:) s cmr10.329 @sf 60 1830 p m (The) 15 (solution) 16 (of) 15 (the) 15 (original) 17 (problem) 16 (GLM) 14 (can) 16 (b) 1 (e) 16 (written) 15 (in) 16 (the) 15 (forms:) ks cmmi10.329 @sf 718 1932 p m (x) s cmmi8.300 @sf 744 1939 p m (e) s cmr10.329 @sf 775 1932 p m (=) s cmmi10.329 @sf 13 r m (P) s cmr8.300 @sf 852 1939 p m (1) s cmmi10.329 @sf 871 1932 p save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 893 1939 p m (1) s cmr10.329 @sf 913 1932 p m (;) s cmmi10.329 @sf 83 r m (u) s cmmi8.300 @sf 1035 1939 p m (e) s cmr10.329 @sf 1066 1932 p m (=) s cmmi10.329 @sf 13 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr8.300 @sf 1141 1939 p m (2) s cmmi10.329 @sf 1161 1932 p m (v) s cmr8.300 @sf 1183 1939 p m (2) s cmr10.329 @sf 60 2034 p m (or) 15 (in) 16 (a) 15 (more) 14 (straigh) 0 (tforw) -2 (ard) 13 (form) ks cmmi10.329 @sf 652 2136 p m (x) s cmmi8.300 @sf 678 2143 p m (e) s cmr10.329 @sf 709 2136 p m (=) s cmmi10.329 @sf 13 r m (P) s cmr8.300 @sf 786 2143 p m (1) s cmmi10.329 @sf 806 2136 p m (R) s cmsy8.300 @sf 841 2118 p m (\000) s cmr8.300 @sf m (1) s 841 2149 p m (11) s cmr10.329 @sf 888 2136 p m (\() s cmmi10.329 @sf m (Q) s cmr8.300 @sf 942 2118 p m (T) s 942 2147 p m (1) s cmsy10.329 @sf 979 2136 p m (\000) s cmmi10.329 @sf 11 r m (S) s cmr8.300 @sf 1053 2143 p m (12) s cmmi10.329 @sf 1090 2136 p m (S) s cmsy8.300 @sf 1121 2118 p m (\000) s cmr8.300 @sf m (1) s 1118 2149 p m (22) s cmmi10.329 @sf 1167 2136 p m (Q) s cmr8.300 @sf 1203 2118 p m (T) s 1203 2147 p m (2) s cmr10.329 @sf 1231 2136 p m (\)) s cmmi10.329 @sf m (b) s cmr10.329 @sf 60 2238 p m (and) s cmmi10.329 @sf 798 2295 p m (u) s cmmi8.300 @sf 824 2302 p m (e) s cmr10.329 @sf 855 2295 p m (=) s cmmi10.329 @sf 13 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr8.300 @sf 930 2302 p m (2) s cmmi10.329 @sf 949 2295 p m (S) s cmsy8.300 @sf 980 2277 p m (\000) s cmr8.300 @sf m (1) s 977 2307 p m (22) s cmmi10.329 @sf 1027 2295 p m (Q) s cmr8.300 @sf 1063 2277 p m (T) s 1063 2306 p m (2) s cmmi10.329 @sf 1090 2295 p m (b:) s cmbx10.329 @sf 131 2446 p save [<03FFFFC003FFFFC00007E0000007E0000007E0000007E0000007E0000007E0000007E0000007E0 000007E0000007E0000007E0000007E0000007E0000007E0000007E0000007E0000007E000C007 E006C007E006C007E006C007E006E007E00E6007E00C6007E00C7007E01C7C07E07C7FFFFFFC7F FFFFFC> 31 30 -2 0 36] 84 @pc restore 36 r save [ 24 32 -3 0 29] 104 @pc restore 29 r m (e) s 17 r save [<81FF00E7FFC0FE01E0F80070E00078E00038C0003CC0003CC0003C00003C00007C0000FC0007F8 00FFF807FFF00FFFF01FFFE03FFF807FFE007FC000FC0000F80000F00018F00018F00038700038 7000783800F81E03F80FFF3803FC08> 22 31 -3 0 29] 83 @pc restore 29 r m (ensitivit) s save [<1E0000007F800000E1C00000C0E00000FC600000FC300000783000000018000000180000001C00 00001C0000003E0000003E0000007F0000007F000000FF800000F9800001F9C00001F0C00001F0 C00003E0600003E0600007C0300007C030000F8018000F8018001F001C00FFE07F80FFE07F80> 25 29 -1 9 28] 121 @pc restore 44 r m (of) 16 (t) ks save [ 24 32 -3 0 29] 104 @pc restore 29 r m (e) 17 (Problem) ks 14 r save [<0007FC0600003FFF8E0000FE01FE0003F000FE0007E0007E000FC0007E001F80007E003F00007E 003F00007E007F00007E007E00007E007E00007E00FE003FFFE0FE003FFFE0FE00000000FE0000 0000FE00000000FE00000000FE000000007E000006007E000006007F000006003F00000E003F00 000E001F80001E000FC0001E0007E0003E0003F000FE0000FE03DE00003FFF0E000007FC0200> 35 31 -3 0 41] 71 @pc restore 41 r m (L) s save [ 45 31 -2 0 50] 77 @pc restore 50 r m (:) s cmr10.329 @sf 14 r m (Regarding) 16 (to) 13 (the) 15 (sensitivit) 0 (y) 15 (of) 14 (the) 14 (problem) ks 60 2503 p m (solutions) 15 (to) 14 (p) 1 (erturbations,) 14 (w) 0 (e) 14 (shall) 15 (consider) 15 (the) 15 (e\013ects) 14 (of) 14 (the) 14 (p) 1 (erturbations) 15 (in) 15 (the) 15 (v) 0 (ector) ks cmmi10.329 @sf 12 r m (b) s cmr10.329 @sf 60 2559 p m (and) 14 (p) 1 (erturbations) 14 (in) 14 (the) 14 (matrices) ks cmmi10.329 @sf 14 r m (A) s cmr10.329 @sf 13 r m (and) s cmmi10.329 @sf 14 r m (B) s cmr10.329 @sf 2 r m (.) 20 (Let) 14 (the) 14 (p) 1 (erturb) 1 (ed) 14 (problem) 15 (GLM) 13 (b) 1 (e) 14 (de\014ned) 15 (as) ks 431 2661 p m (min) s cmr8.300 @sf 446 2687 p m (\026) s cmmi8.300 @sf 443 2687 p m (x) s 463 2687 p m (;) s cmr8.300 @sf 2 r m (\026) s cmmi8.300 @sf 473 2687 p m (u) s cmr10.329 @sf 517 2661 p m (\026) s cmmi10.329 @sf 514 2661 p m (u) s cmr8.300 @sf 540 2643 p m (T) s cmr10.329 @sf 570 2661 p m (\026) s cmmi10.329 @sf 568 2661 p m (u) s 594 2661 p m (;) s cmr10.329 @sf 45 r m (sub) 3 (ject) 15 (to) ks cmmi10.329 @sf 888 2661 p m (b) s cmr10.329 @sf 10 r m (+) s cmmi10.329 @sf 10 r m (e) s cmr10.329 @sf 13 r m (=) 13 (\() ks cmmi10.329 @sf m (A) s cmr10.329 @sf 10 r m (+) s cmmi10.329 @sf 10 r m (E) s cmr10.329 @sf 3 r m (\)) 3 (\026) ks cmmi10.329 @sf 1207 2661 p m (x) s cmr10.329 @sf 1242 2661 p m (+) 10 (\() ks cmmi10.329 @sf m (B) s cmr10.329 @sf 13 r m (+) s cmmi10.329 @sf 10 r m (F) s cmr10.329 @sf 6 r m (\)) 3 (\026) ks cmmi10.329 @sf 1450 2661 p m (u) s 1477 2661 p m (;) s @eop 12 @bop0 cmbx12.300 @sf [ 20 22 -2 0 25] 122 @dc cmmi10.329 @sf [<0F8000186000301800600C00E00E00E00700E00700E00380E00380E003807001C07001C07001C0 3801C01C01C01E03800F078007FFFE01FFFE007FFE> 23 20 -2 0 26] 27 @dc cmex10.300 @sf [ 10 27 -6 26 23] 13 @dc 12 @bop1 cmsl10.329 @sf 60 -99 p m (The) 15 (Generalized) 17 (QR) 16 (Decomp) 1 (osition) ks cmr10.329 @sf 1037 r m (12) s cmmi10.329 @sf 662 77 p m (B) s cmr8.300 @sf 698 59 p m (+) s cmmi8.300 @sf 696 91 p m (I) 3 (A) ks cmmi10.329 @sf 743 77 p m (z) s cmr10.329 @sf 15 r m (=) s cmmi10.329 @sf 13 r m (Q) s cmex10.300 @sf 871 5 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 998 49 p m (I) s cmsy10.329 @sf 915 106 p m (\000) s cmmi10.329 @sf m (R) s cmsy8.300 @sf 985 88 p m (\000) s cmr8.300 @sf m (1) s 985 118 p m (22) s cmmi10.329 @sf 1033 106 p m (R) s cmr8.300 @sf 1068 113 p m (12) s cmex10.300 @sf 1125 5 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 1157 77 p m (S) s cmsy8.300 @sf 1188 59 p m (\000) s cmr8.300 @sf m (1) s 1185 90 p m (11) s cmmi10.329 @sf 1235 77 p m (z) s cmr10.329 @sf 60 200 p m (where) 17 (w) 0 (e) 16 (do) 18 (not) 16 (form) ks cmmi10.329 @sf 17 r m (R) s cmsy8.300 @sf 555 182 p m (\000) s cmr8.300 @sf m (1) s 555 212 p m (22) s cmr10.329 @sf 619 200 p m (or) s cmmi10.329 @sf 17 r m (S) s cmsy8.300 @sf 708 182 p m (\000) s cmr8.300 @sf m (1) s 705 212 p m (11) s cmr10.329 @sf 772 200 p m (but) 17 (rather) 17 (solv) 0 (e) 16 (the) 17 (triangular) 18 (system) 17 (and) 17 (do) 17 (matrix-) ks 60 256 p m (v) 0 (ector) 13 (op) 1 (erations.) ks cmbx12.300 @sf 60 386 p m (5.) s save [ 21 32 -3 0 28] 50 @pc restore 188 386 p save [<80FF80C7FFE0FF00F8FC003CF0003CE0001EE0001EC0001FC0001FC0001F00003F00003F00007F 0003FF003FFE03FFFE0FFFFC1FFFF83FFFF07FFFC07FFF00FFE000FF0000FC0000FC000CF8000C F8000C78001C78001C7C003C3C007C1F03FC07FF8C01FC04> 24 34 -3 0 31] 83 @pc restore 31 r m (ol) s save [<000E0000000E0000001F0000001F0000003F8000003F8000007FC000007CC000007CC00000F860 0000F8600001F0300001F0300003E0180003E0180007E01C0007C00C000FC00E000F8006000F80 0600FFE01FE0FFE01FE0> 27 22 -1 0 30] 118 @pc restore 29 r m (e) s 17 r save [<0003FF00C0001FFFC3C0007F80E7C001FC003FC003F0001FC007E0001FC00FC0001FC01F80001F C03F00001FC03F00001FC07F00001FC07F00001FC07E000FFFFCFE000FFFFCFE00000000FE0000 0000FE00000000FE00000000FE00000000FE00000000FE000000007E000000C07E000000C07F00 0000C03F000001C03F000001C01F800003C00FC00003C007C00007C003F0000FC001F8003FC000 7F00F1C0001FFFC0C00003FE0040> 38 34 -3 0 44] 71 @pc restore 44 r m (eneralize) s save [<01FC3FC007FF3FC00F83BE001E00FE003E007E007C003E007C003E00FC003E00FC003E00FC003E 00FC003E00FC003E00FC003E00FC003E00FC003E007C003E007E003E003E003E001F007E000F81 FE0007FFBE0001FC3E0000003E0000003E0000003E0000003E0000003E0000003E0000003E0000 003E0000003E0000003E0000003E000001FE000001FE00> 26 35 -2 0 31] 100 @pc restore 47 r save [ 29 34 -2 0 34] 76 @pc restore 34 r m (inear) s 18 r save [ 48 34 -2 0 53] 77 @pc restore 53 r m (o) s 2 r save [<01FC3FC007FF3FC00F83BE001E00FE003E007E007C003E007C003E00FC003E00FC003E00FC003E 00FC003E00FC003E00FC003E00FC003E00FC003E007C003E007E003E003E003E001F007E000F81 FE0007FFBE0001FC3E0000003E0000003E0000003E0000003E0000003E0000003E0000003E0000 003E0000003E0000003E0000003E000001FE000001FE00> 26 35 -2 0 31] 100 @pc restore 31 r m (el) s cmr10.329 @sf 60 480 p m (The) 15 (generalized) 17 (linear) 17 (regression) 15 (mo) 1 (del) 16 (\(Problem) 15 (GLM\)) 15 (can) 15 (b) 1 (e) 16 (written) 15 (as) ks cmmi10.329 @sf 835 582 p m (b) s cmr10.329 @sf 12 r m (=) s cmmi10.329 @sf 13 r m (Ax) s cmr10.329 @sf 10 r m (+) s cmmi10.329 @sf 11 r save [<01F0780007098600060781000E0780800E0380800E0380400E0380400E0380200E0380200E0380 200701C0100701C0100701C0108381C0104380E01841C0E03821C0E0782180E0F8118070F00F00 6060> 29 20 -2 0 33] 119 @pc restore 34 r m (;) s cmr10.329 @sf 1802 582 p m (\(7\)) s 60 685 p m (where) 14 (the) 14 (v) 0 (ector) ks cmmi10.329 @sf 12 r m (b) s cmr10.329 @sf m (,) 13 (the) ks cmmi10.329 @sf 14 r m (n) s cmr10.329 @sf 14 r m (b) 0 (y) ks cmmi10.329 @sf 13 r m (m) s cmr10.329 @sf 14 r m (matrix) s cmmi10.329 @sf 13 r m (A) s cmr10.329 @sf m (,) s cmmi10.329 @sf 14 r m (n) s cmr10.329 @sf 14 r m (b) 0 (y) ks cmmi10.329 @sf 13 r m (n) s cmr10.329 @sf 14 r m (symmetric) 14 (nonnegativ) 0 (e) 13 (de\014nite) 15 (matrix) ks cmmi10.329 @sf 14 r save [<020001000000030001800000070001800000078001C00000078001C0000007C003E0000007C003 F0000007A003D0000007A003C80000079003C80000078803C40000078803C40000078403C20000 078403C20000078203C10000078203C08000078103C08000078183C040000F8083C040000F8043 C020000F0043C020000F0027C010000F00278018000F00178008000F00178004000F000F800400 0F00078002000F00078002000F00078001000F00078001800F8007C003C0FFF03FFC1FF8> 45 32 -2 1 43] 87 @pc restore cmr10.329 @sf 60 741 p m (are) 17 (kno) 0 (wn,) 16 (while) ks cmmi10.329 @sf 19 r save [<01F0780007098600060781000E0780800E0380800E0380400E0380400E0380200E0380200E0380 200701C0100701C0100701C0108381C0104380E01841C0E03821C0E0782180E0F8118070F00F00 6060> 29 20 -2 0 33] 119 @pc restore cmr10.329 @sf 51 r m (is) 17 (a) 17 (random) 17 (error) 17 (with) 17 (mean) 17 (0) 17 (and) 18 (co) 0 (v) -2 (ar) -1 (iance) ks cmmi10.329 @sf 17 r m (\033) s cmr8.300 @sf 1448 726 p m (2) s cmmi10.329 @sf 1467 741 p save [<020001000000030001800000070001800000078001C00000078001C0000007C003E0000007C003 F0000007A003D0000007A003C80000079003C80000078803C40000078803C40000078403C20000 078403C20000078203C10000078203C08000078103C08000078183C040000F8083C040000F8043 C020000F0043C020000F0027C010000F00278018000F00178008000F00178004000F000F800400 0F00078002000F00078002000F00078001000F00078001800F8007C003C0FFF03FFC1FF8> 45 32 -2 1 43] 87 @pc restore cmr10.329 @sf 49 r m (.) 26 (The) 17 (problem) 18 (is) ks 60 797 p m (that) 14 (of) 15 (estimating) 15 (the) 16 (unkno) 0 (wn) 14 (parameters) ks cmmi10.329 @sf 14 r m (x) s cmr10.329 @sf 15 r m (on) 15 (the) 16 (basis) 15 (of) 15 (observ) -2 (ation) ks cmmi10.329 @sf 14 r m (b) s cmr10.329 @sf m (.) 20 (If) ks cmmi10.329 @sf 15 r save [<020001000000030001800000070001800000078001C00000078001C0000007C003E0000007C003 F0000007A003D0000007A003C80000079003C80000078803C40000078803C40000078403C20000 078403C20000078203C10000078203C08000078103C08000078183C040000F8083C040000F8043 C020000F0043C020000F0027C010000F00278018000F00178008000F00178004000F000F800400 0F00078002000F00078002000F00078001000F00078001800F8007C003C0FFF03FFC1FF8> 45 32 -2 1 43] 87 @pc restore cmr10.329 @sf 64 r m (has) 15 (rank) ks cmmi10.329 @sf 60 854 p m (p) s cmr10.329 @sf m (,) 15 (then) ks cmmi10.329 @sf 15 r save [<020001000000030001800000070001800000078001C00000078001C0000007C003E0000007C003 F0000007A003D0000007A003C80000079003C80000078803C40000078803C40000078403C20000 078403C20000078203C10000078203C08000078103C08000078183C040000F8083C040000F8043 C020000F0043C020000F0027C010000F00278018000F00178008000F00178004000F000F800400 0F00078002000F00078002000F00078001000F00078001800F8007C003C0FFF03FFC1FF8> 45 32 -2 1 43] 87 @pc restore cmr10.329 @sf 65 r m (has) 15 (a) 15 (factorization) ks cmmi10.329 @sf 848 910 p save [<020001000000030001800000070001800000078001C00000078001C0000007C003E0000007C003 F0000007A003D0000007A003C80000079003C80000078803C40000078803C40000078403C20000 078403C20000078203C10000078203C08000078103C08000078183C040000F8083C040000F8043 C020000F0043C020000F0027C010000F00278018000F00178008000F00178004000F000F800400 0F00078002000F00078002000F00078001000F00078001800F8007C003C0FFF03FFC1FF8> 45 32 -2 1 43] 87 @pc restore cmr10.329 @sf 62 r m (=) s cmmi10.329 @sf 13 r m (B) 2 (B) ks cmr8.300 @sf 1030 892 p m (T) s cmmi10.329 @sf 1059 910 p m (;) s cmr10.329 @sf 60 994 p m (where) 18 (the) ks cmmi10.329 @sf 18 r m (n) s cmr10.329 @sf 18 r m (b) 0 (y) ks cmmi10.329 @sf 17 r m (p) s cmr10.329 @sf 17 r m (matrix) s cmmi10.329 @sf 18 r m (B) s cmr10.329 @sf 20 r m (has) 18 (linearly) 19 (indep) 1 (en) 1 (den) 0 (t) 19 (columns,) 18 (for) 18 (example,) 19 (the) 17 (Cholesky) ks 60 1050 p m (factorization) 13 (of) ks cmmi10.329 @sf 13 r save [<020001000000030001800000070001800000078001C00000078001C0000007C003E0000007C003 F0000007A003D0000007A003C80000079003C80000078803C40000078803C40000078403C20000 078403C20000078203C10000078203C08000078103C08000078183C040000F8083C040000F8043 C020000F0043C020000F0027C010000F00278018000F00178008000F00178004000F000F800400 0F00078002000F00078002000F00078001000F00078001800F8007C003C0FFF03FFC1FF8> 45 32 -2 1 43] 87 @pc restore cmr10.329 @sf 63 r m (could) 15 (b) 1 (e) 14 (carried) 14 (out) 13 (to) 13 (get) ks cmmi10.329 @sf 13 r m (B) s cmr10.329 @sf 2 r m (.) 20 (In) 15 (some) 13 (practical) 14 (problems,) 14 (the) 14 (matrix) ks cmmi10.329 @sf 13 r m (B) s cmr10.329 @sf 60 1107 p m (migh) 0 (t) 12 (b) 1 (e) 15 (a) 0 (v) -2 (a) -1 (ilable) 14 (directly) -3 (.) 20 (F) -3 (orm) 12 (n) 0 (umerical) 14 (computational) 14 (reasons) 13 (it) 14 (is) 14 (preferable) 14 (to) 13 (use) ks cmmi10.329 @sf 14 r m (B) s cmr10.329 @sf 60 1163 p m (rather) 13 (than) ks cmmi10.329 @sf 14 r save [<020001000000030001800000070001800000078001C00000078001C0000007C003E0000007C003 F0000007A003D0000007A003C80000079003C80000078803C40000078803C40000078403C20000 078403C20000078203C10000078203C08000078103C08000078183C040000F8083C040000F8043 C020000F0043C020000F0027C010000F00278018000F00178008000F00178004000F000F800400 0F00078002000F00078002000F00078001000F00078001800F8007C003C0FFF03FFC1FF8> 45 32 -2 1 43] 87 @pc restore cmr10.329 @sf 49 r m (.) 20 (Since) ks cmmi10.329 @sf 15 r save [<020001000000030001800000070001800000078001C00000078001C0000007C003E0000007C003 F0000007A003D0000007A003C80000079003C80000078803C40000078803C40000078403C20000 078403C20000078203C10000078203C08000078103C08000078183C040000F8083C040000F8043 C020000F0043C020000F0027C010000F00278018000F00178008000F00178004000F000F800400 0F00078002000F00078002000F00078001000F00078001800F8007C003C0FFF03FFC1FF8> 45 32 -2 1 43] 87 @pc restore cmr10.329 @sf 64 r m (could) 15 (b) 1 (e) 14 (ill-c) 1 (onditi) 1 (oned) 16 (in) 15 (the) 14 (sene) 14 (discussed) 16 (b) 0 (y) 13 (Golub) 14 (and) 15 (St) 0 (y) -1 (an) ks 60 1220 p m (\(1973\).) 18 (Then) 16 (the) 15 (condition) 17 (of) ks cmmi10.329 @sf 14 r m (B) s cmr10.329 @sf 18 r m (will) 17 (b) 1 (e) 16 (m) 0 (uc) 0 (h) 13 (b) 1 (etter.) 20 (Th) 0 (us) 14 (w) 0 (e) 14 (replace) 16 (\(7\)) 15 (b) 0 (y) ks cmmi10.329 @sf 821 1322 p m (b) s cmr10.329 @sf 12 r m (=) s cmmi10.329 @sf 13 r m (Ax) s cmr10.329 @sf 10 r m (+) s cmmi10.329 @sf 10 r m (B) 2 (u;) ks cmr10.329 @sf 1802 1322 p m (\(8\)) s 60 1424 p m (where) s cmmi10.329 @sf 12 r m (A) s cmr10.329 @sf 12 r m (is) 12 (a) ks cmmi10.329 @sf 12 r m (n) s cmr10.329 @sf 12 r m (b) 0 (y) ks cmmi10.329 @sf 11 r m (m) s cmr10.329 @sf 11 r m (matrix,) s cmmi10.329 @sf 12 r m (B) s cmr10.329 @sf 15 r m (is) s cmmi10.329 @sf 12 r m (n) s cmr10.329 @sf 12 r m (b) 0 (y) ks cmmi10.329 @sf 11 r m (p) s cmr10.329 @sf 12 r m (matrix) 11 (ha) 0 (ving) 11 (full) 14 (column) 12 (rank,) 12 (while) ks cmmi10.329 @sf 14 r m (u) s cmr10.329 @sf 11 r m (is) 13 (a) 11 (random) ks 60 1480 p m (error) 17 (with) 17 (mean) 18 (0) 17 (and) 17 (co) 0 (v) -2 (ariance) ks cmmi10.329 @sf 16 r m (\033) s cmr8.300 @sf 783 1465 p m (2) s cmmi10.329 @sf 803 1480 p m (I) s cmr10.329 @sf 4 r m (.) 26 (Then) 18 (the) 17 (estimator) 17 (of) ks cmmi10.329 @sf 17 r m (x) s cmr10.329 @sf 17 r m (in) 18 (\() 17 (8\)) 17 (is) 18 (the) 17 (solution) 19 (to) ks 60 1537 p m (the) 15 (follo) 0 (wing) 15 (algebraic) 16 (generalized) 17 (linear) 17 (least) 15 (squares) 15 (problem:) ks 616 1639 p m (min) s cmmi8.300 @sf 629 1664 p m (x;u) s cmmi10.329 @sf 699 1639 p m (u) s cmr8.300 @sf 725 1621 p m (T) s cmmi10.329 @sf 753 1639 p m (u) s cmr10.329 @sf 38 r m (sub) 3 (ject) 15 (to) ks cmmi10.329 @sf 1053 1639 p m (b) s cmr10.329 @sf 12 r m (=) s cmmi10.329 @sf 13 r m (Ax) s cmr10.329 @sf 10 r m (+) s cmmi10.329 @sf 11 r m (B) 2 (u) ks cmr10.329 @sf 1802 1639 p m (\(9\)) s 60 1758 p m (F) -3 (or) 18 (con) 0 (v) -1 (enience,) 20 (w) 0 (e) 18 (assume) 19 (that) ks cmmi10.329 @sf 19 r m (n) s cmsy10.329 @sf 19 r save [ 26 36 -4 7 35] 21 @pc restore cmmi10.329 @sf 55 r m (m) s cmr10.329 @sf m (,) s cmmi10.329 @sf 20 r m (n) s cmsy10.329 @sf 20 r save [ 26 36 -4 7 35] 21 @pc restore cmmi10.329 @sf 55 r m (p) s cmr10.329 @sf m (,) 19 (and) 20 (rank) ks 1260 1758 p m (\() s cmmi10.329 @sf m (B) s cmr10.329 @sf 2 r m (\)) 20 (=) ks cmmi10.329 @sf 20 r m (p) s cmr10.329 @sf m (,) 20 (the) 19 (most) 18 (frequen) 0 (tly) ks 60 1815 p m (o) 1 (curring) 16 (case.) 20 (When) ks cmmi10.329 @sf 15 r m (B) s cmr10.329 @sf 16 r m (=) s cmmi10.329 @sf 13 r m (I) s cmr10.329 @sf 4 r m (,) 14 (\(9\)) 14 (is) 16 (just) 15 (an) 15 (ordinary) 15 (linear) 17 (regression) 15 (problem.) ks 131 1880 p m (The) 13 (Problem) 14 (GLM) 13 (can) 13 (b) 1 (e) 14 (form) 0 (ulated) 12 (as) 13 (the) 13 (problem) 14 (LSE) 14 (whic) 0 (h) 13 (is) 14 (discussed) 15 (in) 14 (the) 13 (last) ks 60 1936 p m (subsection:) s 387 2014 p m (min) s cmex10.300 @sf 471 1940 p m (\015) s 471 1965 p m (\015) s 471 1990 p m (\015) s 471 2015 p m (\015) s 471 2040 p m (\015) s 494 1967 p m (h) s cmr10.329 @sf 534 2014 p m (0) s cmmi10.329 @sf 598 2014 p m (I) s cmex10.300 @sf 643 1967 p m (i) s 682 1942 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 727 1987 p m (x) s 727 2042 p m (u) s cmex10.300 @sf 774 1942 p save [ 12 124 0 122 24] 35 @pc restore 798 1940 p m (\015) s 798 1965 p m (\015) s 798 1990 p m (\015) s 798 2015 p m (\015) s 798 2040 p m (\015) s cmr10.329 @sf 867 2014 p m (sub) 3 (ject) 15 (to) ks cmex10.300 @sf 1111 1967 p m (h) s cmmi10.329 @sf 1151 2014 p m (A) s 1227 2014 p m (B) s cmex10.300 @sf 1284 1967 p m (i) s 1324 1942 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 1369 1987 p m (x) s 1369 2042 p m (u) s cmex10.300 @sf 1416 1942 p save [ 12 124 0 122 24] 35 @pc restore cmr10.329 @sf 1453 2014 p m (=) s cmmi10.329 @sf 13 r m (b:) s cmr10.329 @sf 60 2127 p m (Hence,) 18 (it) 18 (is) 18 (easy) 17 (to) 17 (see) 17 (that) 17 (the) 17 (problem) 18 (GLM) 17 (has) 18 (a) 17 (unique) 19 (solution) 18 (under) 18 (the) 17 (follo) 0 (wing) ks 60 2184 p m (conditions:) s 535 2240 p m (rank) s cmex10.300 @sf 633 2193 p save [<0006000C001800300070006000C001C0018003800300070006000E000C001C001C001800380038 0038003000700070007000700070007000E000E000E000E000E000E000E000E000E000E000E000 E000E000E000E000E000E000E000700070007000700070007000300038003800380018001C001C 000C000E000600070003000380018001C000C00060007000300018000C0006> 15 74 -8 72 25] 16 @pc restore 658 2193 p m (h) s cmmi10.329 @sf 698 2240 p m (A) s 773 2240 p m (B) s cmex10.300 @sf 831 2193 p m (i) s 851 2193 p save [ 15 74 -1 72 25] 17 @pc restore cmr10.329 @sf 888 2240 p m (=) s cmmi10.329 @sf 13 r m (n) s cmr10.329 @sf 38 r m (and) s 1112 2240 p m (rank) s 1202 2240 p m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) 12 (=) ks cmmi10.329 @sf 13 r m (m:) s cmr10.329 @sf 131 2337 p m (T) -3 (o) 13 (a) 0 (v) 0 (o) -1 (id) 14 (the) 16 (o) 0 (v) -1 (erhead) 13 (of) 15 (computation) 15 (cost,) 14 (storage) 14 (and) 16 (p) 1 (ossible) 17 (n) 0 (umerical) 15 (di) ks save [<7FE3FE3FF007007007000700700700070070070007007007000700700700070070070007007007 000700700700070070070007007007000700700700070070070007007007000700700700070070 0700070070070007007007000700700700FFFFFFFF000700700000070070000007007000000700 700000070070000007007000000700F00F000300F00F000380F80F0001C07C060000F04F040000 1F81F800> 36 32 0 0 38] 14 @pc restore 38 r m (cult) 0 (y) 15 (of) ks 60 2394 p m (the) 18 (com) 0 (bination) 17 (of) 18 (the) 18 (matrices) ks cmmi10.329 @sf 18 r m (A) s cmr10.329 @sf 18 r m (and) s cmmi10.329 @sf 18 r m (B) s cmr10.329 @sf 2 r m (,) 19 (it) 18 (is) 18 (not) 18 (suggested) 17 (to) 18 (solv) 0 (e) 17 (the) 18 (problem) 18 (GLM) ks 60 2450 p m (directly) 16 (b) 0 (y) 14 (the) 15 (metho) 1 (d) 15 (of) 14 (the) 15 (problem) 16 (LSE.) 15 (Early) 15 (1979,) 13 (P) 0 (aige) 14 ([) 0 (10) ks 1371 2450 p m (]) 15 (prop) 1 (osed) 15 (t) 0 (w) -1 (o) 12 (steps) 15 (QR) ks 60 2507 p m (decomp) 1 (osition) 17 (approac) 0 (h) 15 (to) 15 (the) 16 (problem) 16 (GLM) 16 (to) 15 (treat) 15 (with) ks cmmi10.329 @sf 16 r m (A) s cmr10.329 @sf 16 r m (and) s cmmi10.329 @sf 16 r m (B) s cmr10.329 @sf 19 r m (separately) -3 (.) 21 (No) 0 (w,) 14 (his) ks 60 2563 p m (approac) 0 (h) 12 (can) 14 (b) 1 (e) 15 (simpli\014ed) 16 (with) 14 (GQR) 14 (factorization) 14 (terminology) -3 (.) 19 (F) -3 (or) 12 (sak) 0 (e) 12 (of) 13 (argumen) 0 (ts,) 12 (w) 0 (e) ks 60 2620 p m (assume) 14 (that) 13 (the) 15 (Problem) 14 (GLM) 14 (has) 14 (unique) 16 (solutions) 15 (of) ks cmmi10.329 @sf 13 r m (x) s cmr10.329 @sf 14 r m (and) s cmmi10.329 @sf 15 r m (u) s cmr10.329 @sf 14 r m (whic) 0 (h) 14 (w) 0 (e) 13 (denote) 14 (b) 0 (y) ks cmmi10.329 @sf 13 r m (x) s cmmi8.300 @sf 1754 2627 p m (e) s cmr10.329 @sf 1787 2620 p m (and) s cmmi10.329 @sf 60 2676 p m (u) s cmmi8.300 @sf 86 2683 p m (e) s cmr10.329 @sf 104 2676 p m (.) s @eop 11 @bop0 cmmi10.329 @sf [ 21 20 -2 0 22] 23 @dc cmr8.300 @sf [<0FE030304018C00CE00EE00E000E000E000C0018003007E0006000380018001C701C701C601830 300FE0> 15 21 -1 0 18] 51 @dc 11 @bop1 cmsl10.329 @sf 60 -99 p m (The) 15 (Generalized) 17 (QR) 16 (Decomp) 1 (osition) ks cmr10.329 @sf 1037 r m (11) s cmbx10.329 @sf 131 45 p save [<03FFFFC003FFFFC00007E0000007E0000007E0000007E0000007E0000007E0000007E0000007E0 000007E0000007E0000007E0000007E0000007E0000007E0000007E0000007E0000007E000C007 E006C007E006C007E006C007E006E007E00E6007E00C6007E00C7007E01C7C07E07C7FFFFFFC7F FFFFFC> 31 30 -2 0 36] 84 @pc restore 36 r save [ 24 32 -3 0 29] 104 @pc restore 29 r m (e) s 12 r save [<81FF00E7FFC0FE01E0F80070E00078E00038C0003CC0003CC0003C00003C00007C0000FC0007F8 00FFF807FFF00FFFF01FFFE03FFF807FFE007FC000FC0000F80000F00018F00018F00038700038 7000783800F81E03F80FFF3803FC08> 22 31 -3 0 29] 83 @pc restore 29 r m (ensitivit) s save [<1E0000007F800000E1C00000C0E00000FC600000FC300000783000000018000000180000001C00 00001C0000003E0000003E0000007F0000007F000000FF800000F9800001F9C00001F0C00001F0 C00003E0600003E0600007C0300007C030000F8018000F8018001F001C00FFE07F80FFE07F80> 25 29 -1 9 28] 121 @pc restore 39 r m (of) 12 (Problem) 9 (L) ks save [<81FF00E7FFC0FE01E0F80070E00078E00038C0003CC0003CC0003C00003C00007C0000FC0007F8 00FFF807FFF00FFFF01FFFE03FFF807FFE007FC000FC0000F80000F00018F00018F00038700038 7000783800F81E03F80FFF3803FC08> 22 31 -3 0 29] 83 @pc restore 29 r m (E:) s cmr10.329 @sf 11 r m (The) 11 (condition) 11 (n) 0 (um) 0 (b) 1 (ers) 9 (of) ks cmmi10.329 @sf 10 r m (A) s cmr10.329 @sf 10 r m (and) s cmmi10.329 @sf 11 r m (B) s cmr10.329 @sf 13 r m (w) 0 (ere) 9 (in) 0 (tro) 1 (duced) ks 60 102 p m (b) 0 (y) 14 (Elden) 16 ([) 0 (3) ks 287 102 p m (]) 14 (to) 14 (assess) 15 (the) 15 (p) 1 (erturbation) 15 (b) 1 (eha) 0 (vior) 14 (of) 14 (the) 15 (Problem) 15 (LSE.) 15 (Sp) 1 (eci\014c) 1 (all) 1 (y) -3 (,) 15 (let) ks cmmi10.329 @sf 15 r m (E) s cmr10.329 @sf 17 r m (b) 1 (e) ks 60 158 p m (an) 14 (error) 14 (matrix) 14 (of) ks cmmi10.329 @sf 15 r m (A) s cmr10.329 @sf m (,) s cmmi10.329 @sf 14 r m (F) s cmr10.329 @sf 21 r m (b) 1 (e) 15 (an) 15 (error) 13 (matrix) 15 (of) ks cmmi10.329 @sf 14 r m (B) s cmr10.329 @sf 2 r m (,) s cmmi10.329 @sf 15 r m (e) s cmr10.329 @sf 14 r m (and) s cmmi10.329 @sf 15 r m (f) s cmr10.329 @sf 20 r m (b) 1 (e) 15 (errors) 14 (of) ks cmmi10.329 @sf 14 r m (b) s cmr10.329 @sf 14 r m (and) s cmmi10.329 @sf 15 r m (d) s cmr10.329 @sf m (,) 13 (resp) 1 (ectiv) 0 (ely) -3 (.) ks 60 214 p m (W) -3 (e) 16 (assume) 17 (that) ks cmmi10.329 @sf 16 r m (B) s cmr10.329 @sf 14 r m (+) s cmmi10.329 @sf 12 r m (F) s cmr10.329 @sf 23 r m (also) 17 (has) 17 (full) 18 (ro) 0 (w) 16 (rank) 16 (and) ks cmsy10.329 @sf 17 r save [<780000000000FC0000600000FE0000F00000FE0001F80000630001F80000010003EC0000008003 E40000008003C40000004007C40000004007C4000000400F82000000200F82000000200F020000 00201F02000000101F01000000101E01000000103E01000000103E01000000083C00800000087C 00800000087C0080000008780080000004780040000004F80040000004F80040000004F0002000 0007F00020000007F00020000003E00020000003E00010000003E00010000003E00018000001C0 000E000000C0000FF00000000007F00000000003F00000000000F8> 45 37 1 2 37] 78 @pc restore cmr10.329 @sf 44 r m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf 11 r m (+) s cmmi10.329 @sf 12 r m (E) s cmr10.329 @sf 3 r m (\)) s cmsy10.329 @sf 10 r save [<400002C00006C00006C00006C00006C00006C00006C00006C00006C00006C00006C00006C00006 C00006C00006C00006C00006C00006C00006C00006C0000660000C60000C3000181C00700F01E0 03FF8000FE00> 23 28 -3 1 30] 92 @pc restore 42 r save [<780000000000FC0000600000FE0000F00000FE0001F80000630001F80000010003EC0000008003 E40000008003C40000004007C40000004007C4000000400F82000000200F82000000200F020000 00201F02000000101F01000000101E01000000103E01000000103E01000000083C00800000087C 00800000087C0080000008780080000004780040000004F80040000004F80040000004F0002000 0007F00020000007F00020000003E00020000003E00010000003E00010000003E00018000001C0 000E000000C0000FF00000000007F00000000003F00000000000F8> 45 37 1 2 37] 78 @pc restore cmr10.329 @sf 44 r m (\() s cmmi10.329 @sf m (B) s cmr10.329 @sf 14 r m (+) s cmmi10.329 @sf 11 r m (F) s cmr10.329 @sf 6 r m (\)) 16 (=) ks cmsy10.329 @sf 16 r save [<000F0038006000E001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C003 8007001E00F8001E000700038001C001C001C001C001C001C001C001C001C001C001C001C001C0 01C001C000E000600038000F> 16 45 -3 11 23] 102 @pc restore cmr10.329 @sf 23 r m (0) s cmsy10.329 @sf save [ 16 45 -3 11 23] 103 @pc restore cmr10.329 @sf 23 r m (.) 24 (Let) 20 (\026) ks cmmi10.329 @sf 1816 214 p m (x) s cmmi8.300 @sf 1842 221 p m (e) s cmr10.329 @sf 60 271 p m (b) 1 (e) 15 (the) 15 (solution) 15 (of) 14 (the) 15 (same) 14 (problem) 15 (with) ks cmmi10.329 @sf 15 r m (A;) 8 (B) 2 (;) 8 (b;) 8 (d) ks cmr10.329 @sf 12 r m (replaced) 15 (b) 0 (y) ks cmmi10.329 @sf 14 r m (A) s cmr10.329 @sf 9 r m (+) s cmmi10.329 @sf 9 r m (E) s cmr10.329 @sf 3 r m (,) s cmmi10.329 @sf 13 r m (B) s cmr10.329 @sf 11 r m (+) s cmmi10.329 @sf 10 r m (F) s cmr10.329 @sf 6 r m (,) s cmmi10.329 @sf 14 r m (b) s cmr10.329 @sf 8 r m (+) s cmmi10.329 @sf 9 r m (e) s cmr10.329 @sf m (,) s cmmi10.329 @sf 15 r m (d) s cmr10.329 @sf 8 r m (+) s cmmi10.329 @sf 9 r m (f) s cmr10.329 @sf 5 r m (,) s 60 327 p m (resp) 1 (ectiv) 0 (ely) -3 (.) 20 (Elden) 16 (uses) 16 (the) 15 (n) 0 (um) 0 (b) 1 (ers) ks cmmi10.329 @sf 497 426 p m (\024) s cmmi8.300 @sf 523 433 p m (B) s cmr10.329 @sf 554 426 p m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) 12 (=) ks cmsy10.329 @sf 13 r m (k) s cmmi10.329 @sf m (A) s cmsy10.329 @sf m (k) 12 (k) ks cmr10.329 @sf m (\() s cmmi10.329 @sf m (A) s save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmr10.329 @sf 36 r m (\)) s cmr8.300 @sf 905 408 p m (+) s cmsy10.329 @sf 933 426 p m (k) s cmmi10.329 @sf m (;) 45 (\024) ks cmmi8.300 @sf 1040 433 p m (A) s cmr10.329 @sf 1069 426 p m (\() s cmmi10.329 @sf m (B) s cmr10.329 @sf 2 r m (\)) 13 (=) ks cmsy10.329 @sf 13 r m (k) s cmmi10.329 @sf m (B) s cmsy10.329 @sf 2 r m (k) 12 (k) ks cmmi10.329 @sf m (B) s cmr8.300 @sf 1355 408 p m (+) s cmmi8.300 @sf 1353 439 p m (I) 3 (A) ks cmsy10.329 @sf 1400 426 p m (k) s cmr10.329 @sf 60 524 p m (to) 15 (measure) 15 (the) 15 (sensitivit) 0 (y) 15 (of) 15 (the) 15 (problem) 16 (LSE,) 16 (where) ks cmmi10.329 @sf 527 622 p save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmr10.329 @sf 49 r m (=) s cmmi10.329 @sf 13 r m (I) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 11 r m (B) s cmr8.300 @sf 739 604 p m (+) s cmmi10.329 @sf 769 622 p m (B) 2 (;) 71 (B) ks cmr8.300 @sf 925 604 p m (+) s cmmi8.300 @sf 923 636 p m (I) 3 (A) ks cmr10.329 @sf 983 622 p m (=) 13 (\() ks cmmi10.329 @sf m (I) s cmsy10.329 @sf 13 r m (\000) s cmr10.329 @sf 10 r m (\() s cmmi10.329 @sf m (A) s save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmr10.329 @sf 36 r m (\)) s cmr8.300 @sf 1233 604 p m (+) s cmmi10.329 @sf 1262 622 p m (A) s cmr10.329 @sf m (\)) s cmmi10.329 @sf m (B) s cmr8.300 @sf 1350 604 p m (+) s cmmi10.329 @sf 1380 622 p m (:) s cmr10.329 @sf 60 721 p m (His) 17 (asymptotic) 17 (p) 1 (erturbation) 17 (b) 1 (ound,) 17 (mo) 1 (di\014ed) 18 (sligh) 0 (tly) 17 (here,) 17 (can) 17 (b) 1 (e) 17 (presen) 0 (ted) 16 (as) 17 (follo) 0 (wing,) ks 60 777 p m (where) 16 (the) 16 (b) 1 (ound) 16 (has) 16 (a) 15 (+) ks cmmi10.329 @sf m (O) s cmr10.329 @sf 1 r m (\() s cmmi10.329 @sf m (\017) s cmr8.300 @sf 638 762 p m (2) s cmr10.329 @sf 658 777 p m (\)) 16 (term) 15 (\(i.e.,) 15 (the) 16 (higher) 16 (order) 16 (of) 15 (the) 16 (p) 1 (erturbation) 16 (matrices) ks cmmi10.329 @sf 16 r m (E) s cmr10.329 @sf 60 834 p m (and) s cmmi10.329 @sf 15 r m (F) s cmr10.329 @sf 6 r m (\)) 16 (has) 15 (not) 15 (b) 1 (een) 16 (written.) ks cmbx10.329 @sf 131 898 p m (Problem) 14 (L) ks save [<81FF00E7FFC0FE01E0F80070E00078E00038C0003CC0003CC0003C00003C00007C0000FC0007F8 00FFF807FFF00FFFF01FFFE03FFF807FFE007FC000FC0000F80000F00018F00018F00038700038 7000783800F81E03F80FFF3803FC08> 22 31 -3 0 29] 83 @pc restore 29 r m (E) 19 (P) 0 (er) -1 (turbation) 17 (Bound:) ks cmsy10.329 @sf 90 979 p m (k) s cmmi10.329 @sf m (x) s cmmi8.300 @sf 139 986 p m (e) s cmsy10.329 @sf 167 979 p m (\000) s cmr10.329 @sf 14 r m (\026) s cmmi10.329 @sf 213 979 p m (x) s cmmi8.300 @sf 239 986 p m (e) s cmsy10.329 @sf 257 979 p m (k) s 90 999 p 190 2 ru 140 1040 p m (k) s cmmi10.329 @sf m (x) s cmmi8.300 @sf 189 1047 p m (e) s cmsy10.329 @sf 207 1040 p m (k) s 298 1009 p save [ 26 36 -4 7 35] 20 @pc restore cmmi10.329 @sf 48 r m (\024) s cmmi8.300 @sf 372 1016 p m (B) s cmr10.329 @sf 402 1009 p m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) s cmex10.300 @sf 480 950 p save [<0000300000600000C0000180000300000700000E00000C0000180000380000300000700000E000 00C00001C0000180000380000380000300000700000600000E00000E00000C00001C00001C0000 1C0000180000380000380000380000380000700000700000700000700000700000700000700000 E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000 E00000E00000E00000E00000E00000E00000E00000E00000700000700000700000700000700000 7000007000003800003800003800003800001800001C00001C00001C00000C00000E00000E0000 06000007000003000003800003800001800001C00000C00000E000007000003000003800001800 000C00000E000007000003000001800000C0000060000030> 20 99 -9 97 31] 18 @pc restore cmsy10.329 @sf 515 979 p m (k) s cmmi10.329 @sf m (E) s cmsy10.329 @sf 3 r m (k) s 515 999 p 82 2 ru 516 1040 p m (k) s cmmi10.329 @sf m (A) s cmsy10.329 @sf m (k) s cmr10.329 @sf 611 1009 p m (+) s cmmi10.329 @sf 11 r m (\027) s cmmi8.300 @sf 679 1016 p m (e) s cmex10.300 @sf 698 950 p save [ 20 99 -1 97 31] 19 @pc restore cmr10.329 @sf 738 1009 p m (+) s cmmi10.329 @sf 11 r m (\024) s cmmi8.300 @sf 810 1016 p m (A) s cmr10.329 @sf 838 1009 p m (\() s cmmi10.329 @sf m (B) s cmr10.329 @sf 2 r m (\)) s cmex10.300 @sf 918 950 p save [<0000300000600000C0000180000300000700000E00000C0000180000380000300000700000E000 00C00001C0000180000380000380000300000700000600000E00000E00000C00001C00001C0000 1C0000180000380000380000380000380000700000700000700000700000700000700000700000 E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000 E00000E00000E00000E00000E00000E00000E00000E00000700000700000700000700000700000 7000007000003800003800003800003800001800001C00001C00001C00000C00000E00000E0000 06000007000003000003800003800001800001C00000C00000E000007000003000003800001800 000C00000E000007000003000001800000C0000060000030> 20 99 -9 97 31] 18 @pc restore cmsy10.329 @sf 954 979 p m (k) s cmmi10.329 @sf m (F) s cmsy10.329 @sf 6 r m (k) s 954 999 p 83 2 ru 954 1040 p m (k) s cmmi10.329 @sf m (B) s cmsy10.329 @sf 2 r m (k) s cmr10.329 @sf 1051 1009 p m (+) s cmmi10.329 @sf 10 r save [<001000001800001800001800000C00000C00000C00000C00000600000600000600000200000200 000200000300000300000300000280000280000280000240000240800420C00420400C10301C10 3FF8101FF8080FF00803E004> 22 30 -1 10 24] 13 @pc restore cmmi8.300 @sf 1120 1016 p m (e) s cmex10.300 @sf 1138 950 p save [ 20 99 -1 97 31] 19 @pc restore cmr10.329 @sf 1179 1009 p m (+) s cmmi10.329 @sf 11 r m (\024) s cmr8.300 @sf 1251 991 p m (2) s cmmi8.300 @sf 1251 1021 p m (B) s cmr10.329 @sf 1281 1009 p m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) s cmex10.300 @sf 1359 950 p save [<0000300000600000C0000180000300000700000E00000C0000180000380000300000700000E000 00C00001C0000180000380000380000300000700000600000E00000E00000C00001C00001C0000 1C0000180000380000380000380000380000700000700000700000700000700000700000700000 E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000 E00000E00000E00000E00000E00000E00000E00000E00000700000700000700000700000700000 7000007000003800003800003800003800001800001C00001C00001C00000C00000E00000E0000 06000007000003000003800003800001800001C00000C00000E000007000003000003800001800 000C00000E000007000003000001800000C0000060000030> 20 99 -9 97 31] 18 @pc restore cmsy10.329 @sf 1394 979 p m (k) s cmmi10.329 @sf m (E) s cmsy10.329 @sf 3 r m (k) s 1394 999 p 82 2 ru 1395 1040 p m (k) s cmmi10.329 @sf m (A) s cmsy10.329 @sf m (k) s cmr10.329 @sf 1490 1009 p m (+) s cmmi10.329 @sf 11 r m (\024) s cmmi8.300 @sf 1562 1016 p m (A) s cmr10.329 @sf 1590 1009 p m (\() s cmmi10.329 @sf m (B) s cmr10.329 @sf 2 r m (\)) s cmsy10.329 @sf 1668 979 p m (k) s cmmi10.329 @sf m (F) s cmsy10.329 @sf 6 r m (k) s 1667 999 p 83 2 ru 1667 1040 p m (k) s cmmi10.329 @sf m (B) s cmsy10.329 @sf 2 r m (k) s cmex10.300 @sf 1755 950 p save [ 20 99 -1 97 31] 19 @pc restore cmmi10.329 @sf 1793 1009 p save [ 21 30 -1 10 24] 26 @pc restore cmmi8.300 @sf 1817 1016 p m (e) s cmr10.329 @sf 60 1129 p m (where) s cmmi10.329 @sf 610 1198 p m (\027) s cmmi8.300 @sf 632 1205 p m (e) s cmr10.329 @sf 664 1198 p m (=) s cmsy10.329 @sf 774 1168 p m (k) s cmmi10.329 @sf m (e) s cmsy10.329 @sf m (k) s 717 1188 p 183 2 ru 717 1230 p m (k) s cmmi10.329 @sf m (A) s cmsy10.329 @sf m (k) 12 (k) ks cmmi10.329 @sf m (x) s cmmi8.300 @sf 858 1237 p m (e) s cmsy10.329 @sf 876 1230 p m (k) s cmmi10.329 @sf 904 1198 p m (;) s 45 r save [<001000001800001800001800000C00000C00000C00000C00000600000600000600000200000200 000200000300000300000300000280000280000280000240000240800420C00420400C10301C10 3FF8101FF8080FF00803E004> 22 30 -1 10 24] 13 @pc restore cmmi8.300 @sf 986 1205 p m (e) s cmr10.329 @sf 1016 1198 p m (=) s cmsy10.329 @sf 1126 1168 p m (k) s cmmi10.329 @sf m (f) s cmsy10.329 @sf 5 r m (k) s 1069 1188 p 185 2 ru 1069 1230 p m (k) s cmmi10.329 @sf m (B) s cmsy10.329 @sf 2 r m (k) 13 (k) ks cmmi10.329 @sf m (x) s cmmi8.300 @sf 1213 1237 p m (e) s cmsy10.329 @sf 1231 1230 p m (k) s cmmi10.329 @sf 1259 1198 p m (;) s 651 1335 p save [ 21 30 -1 10 24] 26 @pc restore cmmi8.300 @sf 675 1342 p m (e) s cmr10.329 @sf 705 1335 p m (=) s cmsy10.329 @sf 807 1305 p m (k) s cmmi10.329 @sf m (r) s cmmi8.300 @sf 851 1312 p m (e) s cmsy10.329 @sf 869 1305 p m (k) s 758 1325 p 183 2 ru 758 1366 p m (k) s cmmi10.329 @sf m (A) s cmsy10.329 @sf m (k) 12 (k) ks cmmi10.329 @sf m (x) s cmmi8.300 @sf 899 1373 p m (e) s cmsy10.329 @sf 918 1366 p m (k) s cmmi10.329 @sf 945 1335 p m (;) 45 (r) ks cmmi8.300 @sf 1024 1342 p m (e) s cmr10.329 @sf 1055 1335 p m (=) s cmmi10.329 @sf 13 r m (Ax) s cmmi8.300 @sf 1163 1342 p m (e) s cmsy10.329 @sf 1192 1335 p m (\000) s cmmi10.329 @sf 10 r m (b:) s cmr10.329 @sf 131 1449 p m (The) 15 (in) 0 (terpretation) 15 (of) 15 (this) 16 (result) 16 (is) 16 (that) 14 (the) 16 (sensitivit) 0 (y) 16 (of) 17 (\026) ks cmmi10.329 @sf 1274 1449 p m (x) s cmmi8.300 @sf 1300 1456 p m (e) s cmr10.329 @sf 1333 1449 p m (is) 16 (measured) 16 (b) 0 (y) ks cmmi10.329 @sf 14 r m (\024) s cmmi8.300 @sf 1671 1456 p m (B) s cmr10.329 @sf 1702 1449 p m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) 15 (and) ks cmmi10.329 @sf 60 1506 p m (\024) s cmmi8.300 @sf 86 1513 p m (A) s cmr10.329 @sf 115 1506 p m (\() s cmmi10.329 @sf m (B) s cmr10.329 @sf 2 r m (\)) 15 (if) 16 (the) 15 (residual) ks cmmi10.329 @sf 16 r m (r) s cmmi8.300 @sf 512 1513 p m (e) s cmr10.329 @sf 546 1506 p m (is) 15 (zero) 15 (or) 15 (relativ) 0 (ely) 15 (small,) 16 (and) 15 (otherwise) 16 (b) 0 (y) ks cmmi10.329 @sf 14 r m (\024) s cmr8.300 @sf 1453 1491 p m (2) s cmmi8.300 @sf 1453 1519 p m (B) s cmr10.329 @sf 1483 1506 p m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)\() s cmmi10.329 @sf m (\024) s cmmi8.300 @sf 1597 1513 p m (A) s cmr10.329 @sf 1625 1506 p m (\() s cmmi10.329 @sf m (B) s cmr10.329 @sf 2 r m (\)) 10 (+) 11 (1\).) ks 131 1570 p m (W) -3 (e) 19 (note) 20 (that) 20 (if) 21 (matrix) ks cmmi10.329 @sf 20 r m (B) s cmr10.329 @sf 23 r m (is) 21 (zero) 21 (\(hence) ks cmmi10.329 @sf 21 r m (F) s cmr10.329 @sf 28 r m (=) 21 (0\),) 21 (then) 21 (the) 21 (problem) 21 (LSE) 21 (is) 21 (just) 20 (the) ks 60 1627 p m (ordinary) 14 (linear) 16 (least) 14 (square) 14 (problem.) 20 (The) 15 (p) 1 (erturbation) 14 (b) 1 (ound) 15 (for) 14 (the) 14 (problem) 15 (LSE) 15 (is) 15 (then) ks 60 1683 p m (reduced) 16 (to) ks cmsy10.329 @sf 273 1764 p m (k) s cmmi10.329 @sf m (x) s cmmi8.300 @sf 322 1771 p m (e) s cmsy10.329 @sf 351 1764 p m (\000) s cmr10.329 @sf 13 r m (\026) s cmmi10.329 @sf 396 1764 p m (x) s cmmi8.300 @sf 422 1771 p m (e) s cmsy10.329 @sf 440 1764 p m (k) s 273 1784 p 190 2 ru 323 1825 p m (k) s cmmi10.329 @sf m (x) s cmmi8.300 @sf 372 1832 p m (e) s cmsy10.329 @sf 390 1825 p m (k) s 481 1794 p save [ 26 36 -4 7 35] 20 @pc restore cmmi10.329 @sf 48 r m (\024) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) s cmex10.300 @sf 633 1735 p save [<0000300000600000C0000180000300000700000E00000C0000180000380000300000700000E000 00C00001C0000180000380000380000300000700000600000E00000E00000C00001C00001C0000 1C0000180000380000380000380000380000700000700000700000700000700000700000700000 E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000 E00000E00000E00000E00000E00000E00000E00000E00000700000700000700000700000700000 7000007000003800003800003800003800001800001C00001C00001C00000C00000E00000E0000 06000007000003000003800003800001800001C00000C00000E000007000003000003800001800 000C00000E000007000003000001800000C0000060000030> 20 99 -9 97 31] 18 @pc restore cmsy10.329 @sf 667 1764 p m (k) s cmmi10.329 @sf m (E) s cmsy10.329 @sf 3 r m (k) s 667 1784 p 82 2 ru 668 1825 p m (k) s cmmi10.329 @sf m (A) s cmsy10.329 @sf m (k) s cmr10.329 @sf 764 1794 p m (+) s cmsy10.329 @sf 872 1764 p m (k) s cmmi10.329 @sf m (e) s cmsy10.329 @sf m (k) s 815 1784 p 183 2 ru 815 1825 p m (k) s cmmi10.329 @sf m (A) s cmsy10.329 @sf m (k) 12 (k) ks cmmi10.329 @sf m (x) s cmmi8.300 @sf 956 1832 p m (e) s cmsy10.329 @sf 974 1825 p m (k) s cmex10.300 @sf 1002 1735 p save [ 20 99 -1 97 31] 19 @pc restore cmr10.329 @sf 1042 1794 p m (+) s cmmi10.329 @sf 11 r m (\024) s cmr8.300 @sf 1114 1776 p m (2) s cmr10.329 @sf 1134 1794 p m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) s cmsy10.329 @sf 1209 1764 p m (k) s cmmi10.329 @sf m (E) s cmsy10.329 @sf 3 r m (k) s 1209 1784 p 82 2 ru 1210 1825 p m (k) s cmmi10.329 @sf m (A) s cmsy10.329 @sf m (k) s 1348 1764 p m (k) s cmmi10.329 @sf m (r) s cmmi8.300 @sf 1392 1771 p m (e) s cmsy10.329 @sf 1410 1764 p m (k) s 1300 1784 p 183 2 ru 1300 1825 p m (k) s cmmi10.329 @sf m (A) s cmsy10.329 @sf m (k) 12 (k) ks cmmi10.329 @sf m (x) s cmmi8.300 @sf 1441 1832 p m (e) s cmsy10.329 @sf 1459 1825 p m (k) s cmr10.329 @sf 1497 1794 p m (+) s cmmi10.329 @sf 10 r m (O) s cmr10.329 @sf 1 r m (\() s cmmi10.329 @sf m (\017) s cmr8.300 @sf 1614 1776 p m (2) s cmr10.329 @sf 1634 1794 p m (\)) s 60 1919 p m (where) s cmmi10.329 @sf 16 r m (\024) s cmmi8.300 @sf 218 1926 p m (B) s cmr10.329 @sf 249 1919 p m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) 13 (=) ks cmmi10.329 @sf 15 r m (\024) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) 14 (=) ks cmsy10.329 @sf 14 r m (k) s cmmi10.329 @sf m (A) s cmsy10.329 @sf m (k) 14 (k) ks cmmi10.329 @sf m (A) s cmr8.300 @sf 692 1904 p m (+) s cmsy10.329 @sf 721 1919 p m (k) s cmr10.329 @sf m (.) 23 (This) 16 (is) 17 (just) 16 (the) 16 (p) 1 (erturbation) 17 (b) 1 (ound) 17 (of) 15 (the) 16 (linear) 18 (least) ks 60 1976 p m (square) 15 (problem) 16 (eariest) 15 (othe) 15 (btained) 16 (b) 0 (y) 15 (Golub) 15 (and) 16 (Wilkinson\(1966\)) 15 ([) 0 (4) ks 1454 1976 p m (].) s cmbx10.329 @sf 131 2041 p m (Esitmation) 23 (of) 23 (t) ks save [ 24 32 -3 0 29] 104 @pc restore 29 r m (e) 23 (condition) 26 (n) 0 (um) -4 (b) 1 (ers:) ks cmr10.329 @sf 28 r m (The) 20 (condition) 22 (n) 0 (um) -1 (b) 1 (ers) 19 (of) 20 (Problem) 20 (LSE) ks cmmi10.329 @sf 60 2097 p m (\024) s cmmi8.300 @sf 86 2104 p m (B) s cmr10.329 @sf 117 2097 p m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) 19 (and) ks cmmi10.329 @sf 21 r m (\024) s cmmi8.300 @sf 326 2104 p m (A) s cmr10.329 @sf 355 2097 p m (\() s cmmi10.329 @sf m (B) s cmr10.329 @sf 2 r m (\)) 20 (in) 0 (v) 0 (olv) 0 (e) ks cmmi10.329 @sf 19 r m (B) s cmr8.300 @sf 642 2082 p m (+) s cmr10.329 @sf 672 2097 p m (,) s cmmi10.329 @sf 21 r m (B) s cmr8.300 @sf 742 2082 p m (+) s cmmi10.329 @sf 773 2097 p m (B) s cmr10.329 @sf 2 r m (,) 22 (\() ks cmmi10.329 @sf m (A) s save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmr10.329 @sf 36 r m (\)) s cmr8.300 @sf 950 2082 p m (+) s cmr10.329 @sf 999 2097 p m (etc,) 21 (and) 21 (computing) 21 (these) 21 (matrices) 21 (can) 20 (b) 1 (e) ks 60 2154 p m (relativ) 0 (ely) 15 (exp) 1 (ensiv) 0 (e.) 21 (F) -3 (ortunately) -3 (,) 13 (it) 16 (is) 15 (p) 1 (ossible) 17 (to) 15 (compute) 15 (inexp) 1 (ensi) 1 (v) 0 (e) 16 (estimates) 15 (of) ks cmmi10.329 @sf 15 r m (\024) s cmmi8.300 @sf 1760 2161 p m (B) s cmr10.329 @sf 1791 2154 p m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) s 60 2210 p m (and) s cmmi10.329 @sf 20 r m (\024) s cmmi8.300 @sf 179 2217 p m (A) s cmr10.329 @sf 208 2210 p m (\() s cmmi10.329 @sf m (B) s cmr10.329 @sf 2 r m (\)) 20 (without) 20 (forming) ks cmmi10.329 @sf 19 r m (B) s cmr8.300 @sf 682 2195 p m (+) s cmr10.329 @sf 713 2210 p m (,) s cmmi10.329 @sf 20 r m (B) s cmr8.300 @sf 782 2195 p m (+) s cmmi10.329 @sf 812 2210 p m (B) s cmr10.329 @sf 23 r m (or) 19 (\() ks cmmi10.329 @sf m (A) s save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmr10.329 @sf 36 r m (\)) s cmr8.300 @sf 1035 2195 p m (+) s cmr10.329 @sf 1064 2210 p m (.) 34 (This) 20 (can) 20 (b) 1 (e) 21 (done) 20 (using) 21 (a) 19 (metho) 1 (d) 20 (of) ks 60 2266 p m (Hager) 14 (\(1984\)) 14 (and) 15 (Higham) 15 (\(1988\)) 13 ([) 0 (5) ks 768 2266 p m (]) 15 (that) 14 (computes) 15 (a) 15 (lo) 0 (w) 0 (er) 13 (b) 1 (ound) 15 (for) ks cmsy10.329 @sf 15 r m (k) s cmmi10.329 @sf m (B) s cmsy10.329 @sf 2 r m (k) s cmsy8.300 @sf 1544 2273 p m (1) s cmr10.329 @sf 1581 2266 p m (,) 15 (where) ks cmmi10.329 @sf 15 r m (B) s cmr10.329 @sf 18 r m (is) 15 (a) ks 60 2323 p m (matrix,) 15 (giv) 0 (en) 15 (a) 15 (mean) 16 (for) 15 (evluating) 16 (matrix-v) 0 (ector) 14 (pro) 1 (ducts) ks cmmi10.329 @sf 16 r m (B) 2 (u) ks cmr10.329 @sf 16 r m (and) s cmmi10.329 @sf 16 r m (B) s cmr8.300 @sf 1445 2308 p m (T) s cmmi10.329 @sf 1473 2323 p m (u) s cmr10.329 @sf m (.) 21 (T) 0 (ypically) -3 (,) 15 (4) 15 (or) 15 (5) ks 60 2379 p m (pro) 1 (ducts) 12 (are) 12 (required,) 13 (and) 12 (the) 13 (lo) 0 (w) -1 (er) 10 (b) 1 (ound) 13 (is) 13 (almost) 11 (alw) 0 (a) -1 (ys) 10 (within) 14 (a) 11 (factor) 11 (3) 12 (of) ks cmsy10.329 @sf 11 r m (k) s cmmi10.329 @sf m (B) s cmsy10.329 @sf 2 r m (k) s cmsy8.300 @sf 1712 2386 p m (1) s cmr10.329 @sf 1750 2379 p m (.) 19 (The) ks 60 2436 p m (corresp) 1 (onding) 18 (subroutine,) 17 (named) 18 (as) ks cmtt10.329 @sf 16 r m (S) s save [<7FFFF0FFFFF07FFFF00E00700E00700E00700E00700E00700E00000E00000E00000E00000E0000 0E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00007FE000 FFE0007FE000> 20 28 -1 0 24] 76 @pc restore 24 r m (ACO) s save [<7F03C0FF87C07F07C01C0DC01C0DC01C0DC01C1DC01C19C01C19C01C39C01C39C01C39C01C31C0 1C71C01C71C01C61C01CE1C01CE1C01CE1C01CC1C01CC1C01DC1C01D81C01D81C01D81C07F07F0 FF0FF87E07F0> 21 28 -1 0 24] 78 @pc restore cmr10.329 @sf 24 r m (,) 15 (is) 18 (a) 0 (v) -2 (a) -1 (ilable) 17 (in) 18 (LAP) -3 (A) 0 (CK.) 15 (T) -3 (o) 15 (estimate) ks cmmi10.329 @sf 17 r m (\024) s cmmi8.300 @sf 1760 2443 p m (B) s cmr10.329 @sf 1791 2436 p m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) s 60 2492 p m (and) s cmmi10.329 @sf 17 r m (\024) s cmmi8.300 @sf 176 2499 p m (A) s cmr10.329 @sf 205 2492 p m (\() s cmmi10.329 @sf m (B) s cmr10.329 @sf 2 r m (\),) 18 (w) 0 (e) 16 (apparen) 0 (tly) 16 (need) 18 (to) 17 (estimate) 17 (v) 0 (ector) 16 (norms) ks cmsy10.329 @sf 16 r m (k) s cmmi10.329 @sf save [ 37 31 -2 0 39] 75 @pc restore 42 r m (z) s cmsy10.329 @sf 2 r m (k) s cmsy8.300 @sf 1344 2499 p m (1) s cmr10.329 @sf 1381 2492 p m (,) 17 (where) ks cmmi10.329 @sf 18 r save [ 37 31 -2 0 39] 75 @pc restore cmr10.329 @sf 58 r m (=) 16 (\() ks cmmi10.329 @sf m (A) s save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmr10.329 @sf 36 r m (\)) s cmr8.300 @sf 1760 2477 p m (+) s cmr10.329 @sf 1789 2492 p m (,) 17 (or) ks cmmi10.329 @sf 60 2549 p save [ 37 31 -2 0 39] 75 @pc restore cmr10.329 @sf 58 r m (=) s cmmi10.329 @sf 17 r m (B) s cmr8.300 @sf 206 2531 p m (+) s cmmi8.300 @sf 204 2562 p m (I) 3 (A) ks cmr10.329 @sf 268 2549 p m (and) s cmmi10.329 @sf 17 r m (z) s cmsy10.329 @sf 19 r save [ 26 36 -4 7 35] 21 @pc restore cmr10.329 @sf 51 r m (0) 17 (is) 18 (a) 17 (v) 0 (ector) 16 (that) 16 (is) 18 (readily) 19 (computed.) 26 (Giv) 0 (en) 17 (GQR) 18 (factorization) 17 (of) ks cmmi10.329 @sf 17 r m (A) s cmr10.329 @sf 60 2605 p m (and) s cmmi10.329 @sf 15 r m (B) s cmr10.329 @sf 2 r m (,) 16 (after) 14 (tedious) 16 (computations,) 15 (w) 0 (e) 14 (ha) 0 (v) -1 (e) ks 739 2704 p m (\() s cmmi10.329 @sf m (A) s save [<007F00000380C100060033000C000B801C000F803800078038000780700003C0700003C0700003 C0F00003C0F00001E0F00001E0F0007FFCF0000000780000007800000078000000780000003C00 00003C0000001E0000081E0000080F00000C0700000C0380000C01C0000C00E0000E0070001E00 38002E000E00460003818300007E01> 32 33 -2 1 36] 71 @pc restore cmr10.329 @sf 36 r m (\)) s cmr8.300 @sf 845 2686 p m (+) s cmmi10.329 @sf 873 2704 p m (z) s cmr10.329 @sf 15 r m (=) s cmmi10.329 @sf 13 r m (Q) s cmr8.300 @sf 993 2711 p m (2) s cmmi10.329 @sf 1013 2704 p m (R) s cmsy8.300 @sf 1048 2686 p m (\000) s cmr8.300 @sf m (1) s 1048 2716 p m (22) s cmmi10.329 @sf 1095 2704 p save [<07E000000C18000038040000300200007001000070008000F0004000F0004000F0002000F00020 00F0002000780010007800100078001000780010003C0008003C0008003C0008003C0008001E00 04001E0004001E0004001E0004000F0002000F0002000F0002000F000200078001000780010007 80010007C003C07FFC1FF8> 29 32 -4 1 31] 85 @pc restore cmr8.300 @sf 1131 2686 p m (T) s 1126 2715 p m (3) s cmmi10.329 @sf 1158 2704 p m (z) s @eop 10 @bop0 cmex10.300 @sf [ 3 27 -13 26 28] 54 @dc [ 3 27 -11 26 28] 55 @dc cmmi8.300 @sf [<1E00218070C070600060003007B00C7018381818181818180C0C0C0C0C0C860C4606460626061C 02> 15 20 -1 6 17] 121 @dc 1.000000 /cmr6.300 @newfont cmr6.300 @sf [ 11 16 -1 0 15] 50 @dc 10 @bop1 cmsl10.329 @sf 60 -99 p m (The) 15 (Generalized) 17 (QR) 16 (Decomp) 1 (osition) ks cmr10.329 @sf 1037 r m (10) s 131 45 p m (By) 14 (the) 14 (GQR) 14 (factoization) 14 (of) ks cmmi10.329 @sf 14 r m (B) s cmr8.300 @sf 728 30 p m (T) s cmr10.329 @sf 770 45 p m (and) s cmmi10.329 @sf 15 r m (A) s cmr8.300 @sf 892 30 p m (T) s cmr10.329 @sf 919 45 p m (,) 14 (w) 0 (e) 13 (kno) 0 (w) 12 (that) 14 (there) 14 (are) 14 (orthogonal) 13 (matrices) ks cmmi10.329 @sf 14 r m (Q) s cmr10.329 @sf 60 102 p m (and) s cmmi10.329 @sf 15 r save [<07E000000C18000038040000300200007001000070008000F0004000F0004000F0002000F00020 00F0002000780010007800100078001000780010003C0008003C0008003C0008003C0008001E00 04001E0004001E0004001E0004000F0002000F0002000F0002000F000200078001000780010007 80010007C003C07FFC1FF8> 29 32 -4 1 31] 85 @pc restore 275 225 p m (Q) s cmr8.300 @sf 311 209 p m (T) s cmmi10.329 @sf 339 225 p m (A) s cmr8.300 @sf 373 209 p m (T) s cmmi10.329 @sf 400 225 p save [<07E000000C18000038040000300200007001000070008000F0004000F0004000F0002000F00020 00F0002000780010007800100078001000780010003C0008003C0008003C0008003C0008001E00 04001E0004001E0004001E0004000F0002000F0002000F0002000F000200078001000780010007 80010007C003C07FFC1FF8> 29 32 -4 1 31] 85 @pc restore cmr10.329 @sf 49 r m (=) s cmex10.300 @sf 544 151 p save [ 12 124 -11 122 24] 34 @pc restore cmr10.329 @sf 589 197 p m (0) s cmmi10.329 @sf 653 197 p m (R) s cmr8.300 @sf 688 180 p m (T) s 688 207 p m (11) s cmmi10.329 @sf 766 197 p m (R) s cmr8.300 @sf 801 180 p m (T) s 801 207 p m (12) s cmr10.329 @sf 589 251 p m (0) s 678 251 p m (0) s cmmi10.329 @sf 766 251 p m (R) s cmr8.300 @sf 801 236 p m (T) s 801 263 p m (22) s cmex10.300 @sf 859 151 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 911 197 p m (p) s 911 251 p m (n) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 11 r m (p) s 546 314 p m (m) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 11 r m (n) s 711 314 p m (p) s 775 314 p m (n) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 11 r m (p) s 1058 252 p m (;) s 1137 225 p m (Q) s cmr8.300 @sf 1173 209 p m (T) s cmmi10.329 @sf 1200 225 p m (B) s cmr8.300 @sf 1236 209 p m (T) s cmr10.329 @sf 1277 225 p m (=) s cmex10.300 @sf 1354 151 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 1399 197 p m (S) s cmr8.300 @sf 1430 181 p m (T) s 1427 207 p m (11) s cmr10.329 @sf 1420 251 p m (0) s cmex10.300 @sf 1485 151 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 1518 197 p m (p) s 1518 251 p m (n) s cmsy10.329 @sf 11 r m (\000) s cmmi10.329 @sf 10 r m (p) s 1420 314 p m (p) s cmr10.329 @sf 60 418 p m (and) 13 (moreo) 0 (v) -1 (er,) 11 (from) 12 (the) 13 (assumptions) 13 (\(4\)) 12 (and) 13 (\(6\),) 12 (w) 0 (e) 12 (kno) 0 (w) ks cmmi10.329 @sf 11 r m (S) s cmr8.300 @sf 1243 403 p m (T) s 1240 430 p m (11) s cmr10.329 @sf 1290 418 p m (and) s cmmi10.329 @sf 13 r m (R) s cmr8.300 @sf 1411 403 p m (T) s 1411 430 p m (22) s cmr10.329 @sf 1461 418 p m (are) 13 (upp) 1 (er) 14 (triangular) ks 60 474 p m (and) 15 (nonsingular.) 21 (If) 16 (w) 0 (e) 14 (partition) ks cmmi10.329 @sf 546 580 p m (Q) s cmr10.329 @sf 12 r m (=) s cmex10.300 @sf 642 533 p m (h) s cmmi10.329 @sf 683 580 p m (Q) s cmr8.300 @sf 719 587 p m (1) s cmmi10.329 @sf 780 580 p m (Q) s cmr8.300 @sf 816 587 p m (2) s cmex10.300 @sf 856 533 p m (i) s cmmi10.329 @sf 883 580 p m (;) s 45 r save [<07E000000C18000038040000300200007001000070008000F0004000F0004000F0002000F00020 00F0002000780010007800100078001000780010003C0008003C0008003C0008003C0008001E00 04001E0004001E0004001E0004000F0002000F0002000F0002000F000200078001000780010007 80010007C003C07FFC1FF8> 29 32 -4 1 31] 85 @pc restore cmr10.329 @sf 49 r m (=) s cmex10.300 @sf 1038 533 p m (h) s cmmi10.329 @sf 1078 580 p save [<07E000000C18000038040000300200007001000070008000F0004000F0004000F0002000F00020 00F0002000780010007800100078001000780010003C0008003C0008003C0008003C0008001E00 04001E0004001E0004001E0004000F0002000F0002000F0002000F000200078001000780010007 80010007C003C07FFC1FF8> 29 32 -4 1 31] 85 @pc restore cmr8.300 @sf 1109 587 p m (1) s cmmi10.329 @sf 1171 580 p save [<07E000000C18000038040000300200007001000070008000F0004000F0004000F0002000F00020 00F0002000780010007800100078001000780010003C0008003C0008003C0008003C0008001E00 04001E0004001E0004001E0004000F0002000F0002000F0002000F000200078001000780010007 80010007C003C07FFC1FF8> 29 32 -4 1 31] 85 @pc restore cmr8.300 @sf 1202 587 p m (2) s cmmi10.329 @sf 1263 580 p save [<07E000000C18000038040000300200007001000070008000F0004000F0004000F0002000F00020 00F0002000780010007800100078001000780010003C0008003C0008003C0008003C0008001E00 04001E0004001E0004001E0004000F0002000F0002000F0002000F000200078001000780010007 80010007C003C07FFC1FF8> 29 32 -4 1 31] 85 @pc restore cmr8.300 @sf 1294 587 p m (3) s cmex10.300 @sf 1334 533 p m (i) s cmmi10.329 @sf 1362 580 p m (;) s cmr10.329 @sf 60 686 p m (where) s cmmi10.329 @sf 15 r m (Q) s cmr8.300 @sf 227 693 p m (1) s cmr10.329 @sf 262 686 p m (has) s cmmi10.329 @sf 15 r m (p) s cmr10.329 @sf 15 r m (columns,) s cmmi10.329 @sf 16 r save [<07E000000C18000038040000300200007001000070008000F0004000F0004000F0002000F00020 00F0002000780010007800100078001000780010003C0008003C0008003C0008003C0008001E00 04001E0004001E0004001E0004000F0002000F0002000F0002000F000200078001000780010007 80010007C003C07FFC1FF8> 29 32 -4 1 31] 85 @pc restore cmr8.300 @sf 602 693 p m (1) s cmr10.329 @sf 637 686 p m (has) s cmmi10.329 @sf 15 r m (m) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (n) s cmr10.329 @sf 16 r m (columns,) 15 (and) ks cmmi10.329 @sf 16 r save [<07E000000C18000038040000300200007001000070008000F0004000F0004000F0002000F00020 00F0002000780010007800100078001000780010003C0008003C0008003C0008003C0008001E00 04001E0004001E0004001E0004000F0002000F0002000F0002000F000200078001000780010007 80010007C003C07FFC1FF8> 29 32 -4 1 31] 85 @pc restore cmr8.300 @sf 1165 693 p m (2) s cmr10.329 @sf 1200 686 p m (has) s cmmi10.329 @sf 15 r m (p) s cmr10.329 @sf 15 r m (columns,) 15 (and) 16 (set) ks cmmi10.329 @sf 398 841 p save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr10.329 @sf 36 r m (=) s cmmi10.329 @sf 13 r m (Q) s cmr8.300 @sf 518 823 p m (T) s cmmi10.329 @sf 546 841 p m (x) s cmr10.329 @sf 13 r m (=) s cmex10.300 @sf 633 769 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 678 814 p save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 700 821 p m (1) s cmmi10.329 @sf 678 869 p save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 700 876 p m (2) s cmex10.300 @sf 740 769 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 793 814 p m (p) s 793 869 p m (n) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 11 r m (p) s 919 841 p m (;) 45 (c) ks cmr10.329 @sf 13 r m (=) s cmmi10.329 @sf 13 r save [<07E000000C18000038040000300200007001000070008000F0004000F0004000F0002000F00020 00F0002000780010007800100078001000780010003C0008003C0008003C0008003C0008001E00 04001E0004001E0004001E0004000F0002000F0002000F0002000F000200078001000780010007 80010007C003C07FFC1FF8> 29 32 -4 1 31] 85 @pc restore cmr8.300 @sf 1094 823 p m (T) s cmmi10.329 @sf 1121 841 p m (b) s cmr10.329 @sf 12 r m (=) s cmex10.300 @sf 1201 744 p save [ 14 74 -13 73 28] 50 @pc restore 1201 817 p m (6) s 1201 844 p save [ 14 74 -13 72 28] 52 @pc restore cmmi10.329 @sf 1250 785 p m (c) s cmr8.300 @sf 1270 792 p m (1) s cmmi10.329 @sf 1250 841 p m (c) s cmr8.300 @sf 1270 848 p m (2) s cmmi10.329 @sf 1250 898 p m (c) s cmr8.300 @sf 1270 905 p m (3) s cmex10.300 @sf 1310 744 p save [<001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C00 1C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C 001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C00 1C001C001C001C001C001C001C001C001C001C001C001C001CFFFCFFFCFFFC> 14 74 0 73 28] 51 @pc restore 1310 817 p m (7) s 1310 844 p save [ 14 74 0 72 28] 53 @pc restore cmmi10.329 @sf 1366 785 p m (m) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (n) s 1366 841 p m (p) s 1366 898 p m (n) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 11 r m (p) s 1509 841 p m (;) s cmr10.329 @sf 60 1004 p m (where) s cmmi10.329 @sf 15 r save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmmi8.300 @sf 213 1011 p m (i) s cmr10.329 @sf 240 1004 p m (=) s cmmi10.329 @sf 13 r m (Q) s cmr8.300 @sf 324 989 p m (T) s cmmi8.300 @sf 324 1016 p m (i) s cmmi10.329 @sf 352 1004 p m (x;) 8 (i) ks cmr10.329 @sf 11 r m (=) 13 (1) ks cmmi10.329 @sf m (;) s cmr10.329 @sf 8 r m (2,) s cmmi10.329 @sf 14 r m (c) s cmmi8.300 @sf 588 1011 p m (i) s cmr10.329 @sf 614 1004 p m (=) s cmmi10.329 @sf 13 r save [<07E000000C18000038040000300200007001000070008000F0004000F0004000F0002000F00020 00F0002000780010007800100078001000780010003C0008003C0008003C0008003C0008001E00 04001E0004001E0004001E0004000F0002000F0002000F0002000F000200078001000780010007 80010007C003C07FFC1FF8> 29 32 -4 1 31] 85 @pc restore cmr8.300 @sf 698 989 p m (T) s cmmi8.300 @sf 693 1016 p m (i) s cmmi10.329 @sf 726 1004 p m (b;) 8 (i) ks cmr10.329 @sf 11 r m (=) 13 (1) ks cmmi10.329 @sf m (;) s cmr10.329 @sf 8 r m (2) s cmmi10.329 @sf m (;) s cmr10.329 @sf 8 r m (3) -1 (.) 18 (The) 16 (Problem) 15 (LSE) 16 (is) 16 (then) 15 (transformed) 14 (to) ks 589 1163 p m (min) s cmex10.300 @sf 672 1064 p m (\015) s 672 1089 p m (\015) s 672 1114 p m (\015) s 672 1139 p m (\015) s 672 1164 p m (\015) s 672 1189 p m (\015) s 672 1214 p m (\015) s 695 1066 p save [ 14 74 -13 73 28] 50 @pc restore 695 1139 p m (6) s 695 1166 p save [ 14 74 -13 72 28] 52 @pc restore cmr10.329 @sf 768 1106 p m (0) s 881 1106 p m (0) s cmmi10.329 @sf 743 1163 p m (R) s cmr8.300 @sf 778 1170 p m (11) s cmr10.329 @sf 881 1163 p m (0) s cmmi10.329 @sf 743 1219 p m (R) s cmr8.300 @sf 778 1226 p m (12) s cmmi10.329 @sf 857 1219 p m (R) s cmr8.300 @sf 892 1226 p m (22) s cmex10.300 @sf 949 1066 p save [<001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C00 1C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C 001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C00 1C001C001C001C001C001C001C001C001C001C001C001C001CFFFCFFFCFFFC> 14 74 0 73 28] 51 @pc restore 949 1139 p m (7) s 949 1166 p save [ 14 74 0 72 28] 53 @pc restore 985 1091 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 1030 1136 p save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 1052 1143 p m (1) s cmmi10.329 @sf 1030 1191 p save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 1052 1198 p m (2) s cmex10.300 @sf 1092 1091 p save [ 12 124 0 122 24] 35 @pc restore cmsy10.329 @sf 1127 1163 p m (\000) s cmex10.300 @sf 1172 1066 p save [ 14 74 -13 73 28] 50 @pc restore 1172 1139 p m (6) s 1172 1166 p save [ 14 74 -13 72 28] 52 @pc restore cmmi10.329 @sf 1221 1106 p m (c) s cmr8.300 @sf 1241 1113 p m (1) s cmmi10.329 @sf 1221 1163 p m (c) s cmr8.300 @sf 1241 1170 p m (2) s cmmi10.329 @sf 1221 1219 p m (c) s cmr8.300 @sf 1241 1226 p m (3) s cmex10.300 @sf 1281 1066 p save [<001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C00 1C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C 001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C00 1C001C001C001C001C001C001C001C001C001C001C001C001CFFFCFFFCFFFC> 14 74 0 73 28] 51 @pc restore 1281 1139 p m (7) s 1281 1166 p save [ 14 74 0 72 28] 53 @pc restore 1308 1064 p m (\015) s 1308 1089 p m (\015) s 1308 1114 p m (\015) s 1308 1139 p m (\015) s 1308 1164 p m (\015) s 1308 1189 p m (\015) s 1308 1214 p m (\015) s cmr10.329 @sf 60 1318 p m (sub) 3 (ject) 15 (to) ks cmex10.300 @sf 737 1358 p m (h) s cmmi10.329 @sf 777 1405 p m (S) s cmr8.300 @sf 805 1412 p m (11) s cmr10.329 @sf 884 1405 p m (0) s cmex10.300 @sf 927 1358 p m (i) s 954 1333 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 999 1378 p save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 1021 1385 p m (1) s cmmi10.329 @sf 999 1433 p save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 1021 1440 p m (2) s cmex10.300 @sf 1062 1333 p save [ 12 124 0 122 24] 35 @pc restore cmr10.329 @sf 1099 1405 p m (=) s cmmi10.329 @sf 13 r m (d:) s cmr10.329 @sf 60 1518 p m (Hence) 16 (w) 0 (e) 14 (can) 15 (compute) ks cmmi10.329 @sf 16 r save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 552 1525 p m (1) s cmr10.329 @sf 587 1518 p m (from) 14 (constrained) 16 (equalit) 0 (y) 15 (b) 0 (y) 14 (solving) 16 (the) 15 (triangular) 16 (system) ks cmmi10.329 @sf 858 1618 p m (S) s cmr8.300 @sf 886 1625 p m (11) s cmmi10.329 @sf 923 1618 p save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 945 1625 p m (1) s cmr10.329 @sf 978 1618 p m (=) s cmmi10.329 @sf 13 r m (d:) s cmr10.329 @sf 60 1719 p m (Then) 16 (the) 15 (Problem) 16 (LSE) 15 (is) 16 (truncated) 15 (to) 15 (the) 15 (ordinary) 15 (linear) 17 (least) 15 (square) 15 (problem) ks 689 1819 p m (min) s cmmi8.300 @sf 709 1844 p m (y) s cmr6.300 @sf 726 1849 p m (2) s cmsy10.329 @sf 772 1819 p m (k) s cmmi10.329 @sf m (R) s cmr8.300 @sf 830 1826 p m (22) s cmmi10.329 @sf 867 1819 p save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 889 1826 p m (2) s cmsy10.329 @sf 919 1819 p m (\000) s cmr10.329 @sf 10 r m (\() s cmmi10.329 @sf m (c) s cmr8.300 @sf 1002 1826 p m (3) s cmsy10.329 @sf 1031 1819 p m (\000) s cmmi10.329 @sf 11 r m (R) s cmr8.300 @sf 1112 1826 p m (12) s cmmi10.329 @sf 1149 1819 p save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 1171 1826 p m (1) s cmr10.329 @sf 1191 1819 p m (\)) s cmsy10.329 @sf m (k) s cmr10.329 @sf 60 1934 p m (Since) s cmmi10.329 @sf 17 r m (R) s cmr8.300 @sf 214 1941 p m (22) s cmr10.329 @sf 266 1934 p m (is) 15 (nonsingular) 17 (and) 15 (lo) 0 (w) 0 (er) 13 (triangular,) ks cmmi10.329 @sf 15 r save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 1011 1941 p m (2) s cmr10.329 @sf 1046 1934 p m (is) 16 (giv) 0 (en) 14 (b) 0 (y) ks cmmi10.329 @sf 739 2035 p save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 761 2042 p m (2) s cmr10.329 @sf 794 2035 p m (=) s cmmi10.329 @sf 13 r m (R) s cmsy8.300 @sf 877 2017 p m (\000) s cmr8.300 @sf m (1) s 877 2047 p m (22) s cmr10.329 @sf 924 2035 p m (\() s cmmi10.329 @sf m (c) s cmr8.300 @sf 962 2042 p m (3) s cmsy10.329 @sf 991 2035 p m (\000) s cmmi10.329 @sf 11 r m (R) s cmr8.300 @sf 1072 2042 p m (12) s cmmi10.329 @sf 1108 2035 p save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 1130 2042 p m (1) s cmr10.329 @sf 1150 2035 p m (\)) s cmmi10.329 @sf m (;) s cmr10.329 @sf 60 2135 p m (a) 15 (triangular) 15 (solv) 0 (er.) 19 (The) 16 (solution) 15 (of) 15 (Problem) 16 (LSE) 16 (is) 15 (then) 16 (giv) 0 (en) 14 (b) 0 (y) ks cmmi10.329 @sf 722 2235 p m (x) s cmmi8.300 @sf 748 2242 p m (e) s cmr10.329 @sf 779 2235 p m (=) s cmmi10.329 @sf 13 r m (Q) s save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr10.329 @sf 36 r m (=) s cmmi10.329 @sf 13 r m (Q) s cmr8.300 @sf 983 2242 p m (1) s cmmi10.329 @sf 1003 2235 p save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 1025 2242 p m (1) s cmr10.329 @sf 1055 2235 p m (+) s cmmi10.329 @sf 10 r m (Q) s cmr8.300 @sf 1136 2242 p m (2) s cmmi10.329 @sf 1156 2235 p save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 1178 2242 p m (2) s cmr10.329 @sf 60 2336 p m (or) 15 (in) 16 (a) 15 (more) 14 (straigh) 0 (tforw) -2 (ard) 13 (form) ks cmmi10.329 @sf 554 2466 p m (x) s cmmi8.300 @sf 580 2473 p m (e) s cmr10.329 @sf 611 2466 p m (=) s cmmi10.329 @sf 13 r m (Q) s cmr8.300 @sf 695 2473 p m (2) s cmmi10.329 @sf 714 2466 p m (R) s cmsy8.300 @sf 749 2448 p m (\000) s cmr8.300 @sf m (1) s 749 2479 p m (22) s cmmi10.329 @sf 796 2466 p save [<07E000000C18000038040000300200007001000070008000F0004000F0004000F0002000F00020 00F0002000780010007800100078001000780010003C0008003C0008003C0008003C0008001E00 04001E0004001E0004001E0004000F0002000F0002000F0002000F000200078001000780010007 80010007C003C07FFC1FF8> 29 32 -4 1 31] 85 @pc restore cmr8.300 @sf 832 2448 p m (T) s 827 2477 p m (3) s cmmi10.329 @sf 860 2466 p m (b) s cmr10.329 @sf 9 r m (+) s cmmi10.329 @sf 11 r m (Q) s cmex10.300 @sf 979 2394 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 1106 2438 p m (I) s cmsy10.329 @sf 1023 2495 p m (\000) s cmmi10.329 @sf m (R) s cmsy8.300 @sf 1093 2477 p m (\000) s cmr8.300 @sf m (1) s 1093 2507 p m (22) s cmmi10.329 @sf 1141 2495 p m (R) s cmr8.300 @sf 1176 2502 p m (12) s cmex10.300 @sf 1233 2394 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 1265 2466 p m (S) s cmsy8.300 @sf 1296 2448 p m (\000) s cmr8.300 @sf m (1) s 1293 2479 p m (11) s cmmi10.329 @sf 1343 2466 p m (d) s cmr10.329 @sf 60 2603 p m (and) 15 (the) 16 (residual) 16 (sum) 15 (of) 15 (squares) ks cmmi10.329 @sf 15 r save [ 21 30 -1 10 24] 26 @pc restore cmr8.300 @sf 729 2588 p m (2) s cmr10.329 @sf 761 2603 p m (=) s cmsy10.329 @sf 13 r m (k) s cmmi10.329 @sf m (r) s cmmi8.300 @sf 853 2610 p m (e) s cmsy10.329 @sf 871 2603 p m (k) s cmr8.300 @sf 894 2588 p m (2) s cmr10.329 @sf 926 2603 p m (=) s cmsy10.329 @sf 13 r m (k) s cmmi10.329 @sf m (Ax) s cmmi8.300 @sf 1057 2610 p m (e) s cmsy10.329 @sf 1085 2603 p m (\000) s cmmi10.329 @sf 11 r m (b) s cmsy10.329 @sf m (k) s cmr8.300 @sf 1174 2588 p m (2) s cmr10.329 @sf 1208 2603 p m (is) 15 (giv) 0 (en) 15 (b) 0 (y) ks cmmi10.329 @sf 685 2704 p save [ 21 30 -1 10 24] 26 @pc restore cmr8.300 @sf 709 2686 p m (2) s cmr10.329 @sf 741 2704 p m (=) s cmsy10.329 @sf 13 r m (k) s cmmi10.329 @sf m (c) s cmr8.300 @sf 832 2711 p m (1) s cmsy10.329 @sf 851 2704 p m (k) s cmr8.300 @sf 874 2686 p m (2) s cmr10.329 @sf 903 2704 p m (+) s cmsy10.329 @sf 11 r m (k) s cmmi10.329 @sf m (R) s cmr8.300 @sf 1007 2711 p m (11) s cmmi10.329 @sf 1043 2704 p save [<1F000021C000606000707000783800781800001C00000E00000E0003EE00061E000E0F000C0700 0C07000E07000E03800E03800E03800E03800701C00701C00701C08381C04380E041C0E021C0E0 2180E01180700F0060> 20 29 -2 9 22] 121 @pc restore cmr8.300 @sf 1065 2711 p m (1) s cmsy10.329 @sf 1095 2704 p m (\000) s cmmi10.329 @sf 11 r m (c) s cmr8.300 @sf 1161 2711 p m (2) s cmsy10.329 @sf 1180 2704 p m (k) s cmr8.300 @sf 1203 2686 p m (2) s cmmi10.329 @sf 1223 2704 p m (:) s @eop 9 @bop0 cmsy10.329 @sf [<01800180018001800180C183F18F399C0FF003C003C00FF0399CF18FC183018001800180018001 80> 16 20 -3 -1 23] 3 @dc cmr8.300 @sf [ 22 10 -2 -3 27] 61 @dc [<07C01830301070086000E000E000E000FFF8E0187038303018600FC0> 13 14 -1 0 16] 101 @dc 9 @bop1 cmsl10.329 @sf 60 -99 p m (The) 15 (Generalized) 17 (QR) 16 (Decomp) 1 (osition) ks cmr10.329 @sf 1059 r m (9) s 131 45 p m (T) -3 (o) 14 (n) 0 (umerically) 17 (determine) 17 (the) 16 (rank) 16 (of) ks cmmi10.329 @sf 16 r m (A) s cmr10.329 @sf m (,) 16 (according) 16 (to) 15 (the) 17 (prop) 1 (erties) 16 (of) 16 (the) 16 (QR) 17 (factor-) ks 60 102 p m (ization) 16 (with) 16 (column) 16 (piv) 0 (oting,) 14 (w) 0 (e) 14 (can) 15 (use) 16 (the) 15 (the) 15 (follo) 0 (wing) 15 (simple) 17 (strategy:) ks cmmi10.329 @sf 611 200 p m (q) s cmr10.329 @sf 15 r m (=) 13 (0;) ks cmmi10.329 @sf 611 256 p save [<600F00E01880701880703840703840703840381C203838003838003870001FC0001E00001D0000 1C80000E40600E20F00E10F00E08700706100701E0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 20 32 -2 0 24] 107 @pc restore cmr10.329 @sf 38 r m (=) 13 (min) ks 773 256 p m (\() s cmmi10.329 @sf m (n;) 8 (m) ks cmr10.329 @sf m (\);) s 611 313 p m (for) s cmmi10.329 @sf 691 313 p m (i) s cmr10.329 @sf 12 r m (=) 13 (1) ks cmmi10.329 @sf m (;) 8 (m) ks cmr10.329 @sf 690 369 p m (if) s 741 369 p m (\() s cmsy10.329 @sf save [ 2 45 -5 11 13] 106 @pc restore cmmi10.329 @sf 13 r m (r) s cmmi8.300 @sf 793 376 p m (ii) s cmsy10.329 @sf 818 369 p save [ 2 45 -5 11 13] 106 @pc restore 25 r save [ 26 36 -4 7 35] 20 @pc restore cmmi10.329 @sf 48 r m (t) s save [<07C000187000301800700E00700F00F00700F00780F003C0F003C0F003C07801E07801E07801E0 3C01E01C01E01E01C00E01C003018001C300007C00> 19 20 -2 0 22] 111 @pc restore 22 r save [<38006400E200E200E200E200710070007000700038003800380038001C001C001C001C000E000E 000E000E00070007000700070003800380038003801FC003C0> 10 32 -2 0 14] 108 @pc restore cmsy10.329 @sf 25 r m (\003) s 10 r save [ 2 45 -5 11 13] 106 @pc restore cmmi10.329 @sf 13 r m (r) s cmr8.300 @sf 1021 376 p m (11) s cmsy10.329 @sf 1058 369 p save [ 2 45 -5 11 13] 106 @pc restore cmr10.329 @sf 13 r m (\)) s cmmi10.329 @sf 37 r m (q) s cmr10.329 @sf 15 r m (=) s cmmi10.329 @sf 12 r m (q) s cmr10.329 @sf 13 r m (+) 10 (1) ks 60 467 p m (where) s cmmi10.329 @sf 11 r m (t) s save [<07C000187000301800700E00700F00F00700F00780F003C0F003C0F003C07801E07801E07801E0 3C01E01C01E01E01C00E01C003018001C300007C00> 19 20 -2 0 22] 111 @pc restore 22 r save [<38006400E200E200E200E200710070007000700038003800380038001C001C001C001C000E000E 000E000E00070007000700070003800380038003801FC003C0> 10 32 -2 0 14] 108 @pc restore cmr10.329 @sf 26 r m (is) 12 (a) 11 (user) 11 (giv) 0 (en) 11 (tolerance) 12 (v) -2 (alue,) 11 (for) 11 (example,) ks cmmi10.329 @sf 12 r m (t) s save [<07C000187000301800700E00700F00F00700F00780F003C0F003C0F003C07801E07801E07801E0 3C01E01C01E01E01C00E01C003018001C300007C00> 19 20 -2 0 22] 111 @pc restore 22 r save [<38006400E200E200E200E200710070007000700038003800380038001C001C001C001C000E000E 000E000E00070007000700070003800380038003801FC003C0> 10 32 -2 0 14] 108 @pc restore cmr10.329 @sf 26 r m (can) 12 (b) 1 (e) 11 (c) 0 (hosed) 11 (as) 11 (mac) 0 (hine) 11 (precision.) ks 60 524 p m (As) 17 (a) 16 (more) 16 (careful) 17 (metho) 1 (d) 17 (to) 16 (determine) 18 (the) 17 (rank) 16 (of) 16 (a) 17 (matrix,) 16 (the) 17 (so-called) 18 (rank) 16 (rev) 0 (ealing) ks 60 580 p m (QR) 16 (factorization) 15 (can) 15 (also) 15 (b) 1 (e) 16 (used) 15 (to) 15 (replace) 16 (the) 15 (normal) 15 (column) 16 (piv) 0 (oting) 15 (QR) 16 (sc) 0 (heme[) 0 (4) ks 1784 580 p m (,) 15 (2) ks 1835 580 p m (].) s 131 645 p m (The) 15 (MA) -3 (TLAB) 15 (co) 1 (des) 15 (of) 15 (algorithm) 15 (1,) 15 (2) 15 (and) 15 (3) 15 (are) 15 (in) 16 (App) 1 (endix.) ks cmbx10.432 @sf 60 797 p save [<00FF800003FFF0000FFFF8001F01FE003C007F0078003F8078003F80FC001FC0FE001FC0FE001F E0FE001FE0FE001FE07C001FE018001FE000001FE000001FE000001FC000001FC000001F800C00 3F000E003E000F80FC000FFFF8000E7FC0000E0000000E0000000E0000000E0000000E0000000E 0000000FFE00000FFFC0000FFFE0000FFFF0000FFFF8000FFFFC000FFFFE000F803F000C000300> 27 39 -3 0 34] 53 @pc restore 163 797 p m (A) s save [ 33 39 -2 12 38] 112 @pc restore 38 r save [ 33 39 -2 12 38] 112 @pc restore 38 r m (l) s save [ 15 43 -3 0 20] 105 @pc restore 20 r m (cat) s save [ 15 43 -3 0 20] 105 @pc restore 19 r m (ons) s cmr10.329 @sf 60 906 p m (In) 18 (the) 17 (ab) 1 (o) 0 (v) 0 (e) 15 (sections,) 18 (w) 0 (e) 16 (in) 0 (tro) 1 (duced) 18 (the) 17 (GQR) 18 (factorization) 17 (with) 18 (or) 17 (without) 17 (piv) 0 (oting.) 26 (In) ks 60 963 p m (this) 16 (section,) 17 (as) 15 (examples,) 17 (w) 0 (e) 15 (will) 17 (sho) 0 (w) 15 (that) 15 (the) 16 (GQR) 17 (factorization) 16 (pro) 0 (vide) 15 (a) 16 (simplier) 18 (and) ks 60 1019 p m (more) 16 (e) ks save [<7FE3FE3FF007007007000700700700070070070007007007000700700700070070070007007007 000700700700070070070007007007000700700700070070070007007007000700700700070070 0700070070070007007007000700700700FFFFFFFF000700700000070070000007007000000700 700000070070000007007000000700F00F000300F00F000380F80F0001C07C060000F04F040000 1F81F800> 36 32 0 0 38] 14 @pc restore 38 r m (cien) 0 (t) 16 (w) 0 (a) -1 (y) 14 (to) 15 (solv) 0 (e) 16 (the) 16 (linear) 17 (equalit) 0 (y) 16 (constrained) 17 (linear) 18 (least) 16 (square) 16 (problem) 17 (and) ks 60 1076 p m (generalized) 14 (linear) 14 (regression) 12 (problem,) 13 (and) 13 (to) 11 (assess) 12 (the) 13 (conditioning) 14 (of) 12 (these) 12 (problems.) 20 (The) ks 60 1132 p m (results) 15 (presen) 0 (ted) 14 (in) 15 (this) 15 (section) 15 (sho) 0 (w) 12 (that) 14 (the) 15 (GQR) 14 (factorization) 15 (for) 13 (solving) 16 (these) 14 (general-) ks 60 1189 p m (ized) 16 (optimization) 16 (or) 14 (linear) 16 (regression) 15 (problems) 15 (is) 15 (just) 15 (as) 14 (p) 1 (o) 0 (w) 0 (er) 12 (as) 15 (the) 14 (QR) 16 (factorization) 15 (for) ks 60 1245 p m (solving) 16 (least) 15 (square) 15 (and) 16 (linear) 16 (regression) 16 (problems.) ks cmbx12.300 @sf 60 1375 p m (5.) s save [<7FFFE07FFFE001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F800 01F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F800 01F800FFF800FFF80001F800007800001800> 19 32 -4 0 28] 49 @pc restore 188 1375 p save [ 29 34 -2 0 34] 76 @pc restore 34 r m (inear) s 17 r save [ 32 34 -2 0 37] 69 @pc restore 37 r save [<0000FFE00000FFE000001F0000001F0000001F0000001F0000001F0000001F0000001F0000001F 0001FC1F0007FF9F000FC1DF001F007F003E003F007E001F007E001F00FC001F00FC001F00FC00 1F00FC001F00FC001F00FC001F00FC001F007C001F007E001F007E003F003F003F001F006F000F C1C70007FF870000FE0300> 27 32 -2 10 30] 113 @pc restore 30 r save [<01FC3FC007FF3FC00F81BE001F00FE001F007E001F003E001F003E001F003E001F003E001F003E 001F003E001F003E001F003E001F003E001F003E001F003E001F003E001F003E001F003E001F00 3E00FF01FE00FF01FE00> 26 22 -2 0 31] 117 @pc restore 31 r m (alit) s -1 r save [<1F0000007F80000069C00000FC600000FC300000FC3800007818000000180000000C0000000C00 00000E0000000E0000001F0000001F0000003F8000003F8000007FC000007CC000007CC00000F8 600000F8600001F0300001F0300003E0180003E0180007E01C0007C00C000FC00E000F8006000F 800600FFE01FE0FFE01FE0> 27 32 -1 10 30] 121 @pc restore 47 r save [<0003FE0000001FFFC00000FF00F00001F800380003F0000C0007C00006000F800003001F800003 003F000003803F000001807F000001807E000001807E00000000FE00000000FE00000000FE0000 0000FE00000000FE00000000FE00000000FE00000000FE000000007E000001807E000001807F00 0001803F000003803F000003801F800007800F8000078007C0000F8003E0001F8001F8003F8000 FF01E380001FFF81800003FE0080> 33 34 -3 0 40] 67 @pc restore 40 r m (onstraine) s save [<01FC3FC007FF3FC00F83BE001E00FE003E007E007C003E007C003E00FC003E00FC003E00FC003E 00FC003E00FC003E00FC003E00FC003E00FC003E007C003E007E003E003E003E001F007E000F81 FE0007FFBE0001FC3E0000003E0000003E0000003E0000003E0000003E0000003E0000003E0000 003E0000003E0000003E0000003E000001FE000001FE00> 26 35 -2 0 31] 100 @pc restore 49 r save [ 29 34 -2 0 34] 76 @pc restore 34 r m (inear) s 18 r save [ 29 34 -2 0 34] 76 @pc restore 34 r m (east) s 18 r save [<80FF80C7FFE0FF00F8FC003CF0003CE0001EE0001EC0001FC0001FC0001F00003F00003F00007F 0003FF003FFE03FFFE0FFFFC1FFFF83FFFF07FFFC07FFF00FFE000FF0000FC0000FC000CF8000C F8000C78001C78001C7C003C3C007C1F03FC07FF8C01FC04> 24 34 -3 0 31] 83 @pc restore 31 r save [<0000FFE00000FFE000001F0000001F0000001F0000001F0000001F0000001F0000001F0000001F 0001FC1F0007FF9F000FC1DF001F007F003E003F007E001F007E001F00FC001F00FC001F00FC00 1F00FC001F00FC001F00FC001F00FC001F007C001F007E001F007E003F003F003F001F006F000F C1C70007FF870000FE0300> 27 32 -2 10 30] 113 @pc restore 30 r save [<01FC3FC007FF3FC00F81BE001F00FE001F007E001F003E001F003E001F003E001F003E001F003E 001F003E001F003E001F003E001F003E001F003E001F003E001F003E001F003E001F003E001F00 3E00FF01FE00FF01FE00> 26 22 -2 0 31] 117 @pc restore 31 r m (ares) s cmr10.329 @sf 60 1469 p m (Linear) 12 (equalit) 0 (y) 10 (constrained) 11 (linear) 12 (least) 10 (squares) 11 (problem) 11 (\(Problem) 10 (LSE\)) 11 (arises) 11 (in) 11 (constrained) ks 60 1526 p m (surface) 12 (\014tting,) 12 (constrained) 12 (optimizing,) 13 (geo) 1 (detic) 13 (least-squares) 12 (adjustmen) 0 (t,) 10 (and) 12 (b) 1 (eamforming) ks 60 1582 p m (etc.) 20 (The) 15 (problem) 16 (is) 16 (stated) 15 (as) 14 (follo) 0 (ws:) 19 (\014nd) 16 (a) ks cmmi10.329 @sf 15 r m (n) s cmr10.329 @sf m (-v) 0 (ector) ks cmmi10.329 @sf 14 r m (x) s cmr10.329 @sf 15 r m (that) 15 (solv) 0 (es) ks 822 1684 p m (min) s cmmi8.300 @sf 813 1714 p m (B) 2 (x) ks cmr8.300 @sf m (=) s cmmi8.300 @sf save [<387046C8C1C480C480C480C0C060C060C06060606070307018F007300018001800180018000C00 0C000C000C003E> 15 23 -2 0 18] 100 @pc restore cmsy10.329 @sf 914 1684 p m (k) s cmmi10.329 @sf m (Ax) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (b) s cmsy10.329 @sf m (k) s cmmi10.329 @sf m (;) s cmr10.329 @sf 1802 1684 p m (\(4\)) s 60 1800 p m (where) s cmmi10.329 @sf 16 r m (A) s cmr10.329 @sf 16 r m (is) s cmmi10.329 @sf 16 r m (m) s cmr10.329 @sf 16 r m (b) 0 (y) ks cmmi10.329 @sf 15 r m (n) s cmr10.329 @sf 16 r m (matrix,) s cmmi10.329 @sf 15 r m (m) s cmsy10.329 @sf 13 r save [ 26 36 -4 7 35] 21 @pc restore cmmi10.329 @sf 49 r m (n) s cmr10.329 @sf m (,) s cmmi10.329 @sf 16 r m (B) s cmr10.329 @sf 19 r m (is) s cmmi10.329 @sf 16 r m (p) s cmr10.329 @sf 16 r m (b) 0 (y) ks cmmi10.329 @sf 15 r m (n) s cmr10.329 @sf 16 r m (matrix,) s cmmi10.329 @sf 15 r m (p) s cmsy10.329 @sf 13 r save [ 26 36 -4 7 35] 20 @pc restore cmmi10.329 @sf 49 r m (n) s cmr10.329 @sf m (,) s cmmi10.329 @sf 16 r m (b) s cmr10.329 @sf 15 r m (is) s cmmi10.329 @sf 17 r m (n) s cmr10.329 @sf 16 r m (column) 16 (v) 0 (ector,) ks cmmi10.329 @sf 14 r m (d) s cmr10.329 @sf 16 r m (is) s cmmi10.329 @sf 16 r m (p) s cmr10.329 @sf 60 1856 p m (column) 15 (v) 0 (ector.) 18 (Clearly) -3 (,) 14 (the) 14 (Problem) 15 (LSE) 15 (has) 14 (a) 14 (solution) 15 (if) 14 (and) 15 (only) 14 (if) 15 (the) 14 (equation) ks cmmi10.329 @sf 15 r m (B) 2 (x) ks cmr10.329 @sf 13 r m (=) s cmmi10.329 @sf 13 r m (d) s cmr10.329 @sf 60 1913 p m (is) 16 (consisten) 0 (t.) 19 (In) 16 (addition,) 15 (for) 15 (simplici) 1 (t) 0 (y) -3 (,) 14 (w) 0 (e) 14 (will) 17 (also) 15 (assume) 15 (that) ks 837 2015 p m (rank) s 927 2015 p m (\() s cmmi10.329 @sf m (B) s cmr10.329 @sf 2 r m (\)) 13 (=) ks cmmi10.329 @sf 13 r m (p) s cmr10.329 @sf 1802 2015 p m (\(5\)) s 60 2117 p m (and) 15 (that) 15 (the) 15 (n) 0 (ull) 16 (spaces) 15 (of) ks cmmi10.329 @sf 15 r m (A) s cmr10.329 @sf 15 r m (and) s cmmi10.329 @sf 16 r m (B) s cmr10.329 @sf 17 r m (in) 0 (tersect) 15 (only) 16 (trivially:) ks cmsy10.329 @sf 506 2249 p save [<780000000000FC0000600000FE0000F00000FE0001F80000630001F80000010003EC0000008003 E40000008003C40000004007C40000004007C4000000400F82000000200F82000000200F020000 00201F02000000101F01000000101E01000000103E01000000103E01000000083C00800000087C 00800000087C0080000008780080000004780040000004F80040000004F80040000004F0002000 0007F00020000007F00020000003E00020000003E00010000003E00010000003E00018000001C0 000E000000C0000FF00000000007F00000000003F00000000000F8> 45 37 1 2 37] 78 @pc restore cmr10.329 @sf 44 r m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\)) s cmsy10.329 @sf 10 r save [<400002C00006C00006C00006C00006C00006C00006C00006C00006C00006C00006C00006C00006 C00006C00006C00006C00006C00006C00006C00006C0000660000C60000C3000181C00700F01E0 03FF8000FE00> 23 28 -3 1 30] 92 @pc restore 40 r save [<780000000000FC0000600000FE0000F00000FE0001F80000630001F80000010003EC0000008003 E40000008003C40000004007C40000004007C4000000400F82000000200F82000000200F020000 00201F02000000101F01000000101E01000000103E01000000103E01000000083C00800000087C 00800000087C0080000008780080000004780040000004F80040000004F80040000004F0002000 0007F00020000007F00020000003E00020000003E00010000003E00010000003E00018000001C0 000E000000C0000FF00000000007F00000000003F00000000000F8> 45 37 1 2 37] 78 @pc restore cmr10.329 @sf 44 r m (\() s cmmi10.329 @sf m (B) s cmr10.329 @sf 2 r m (\)) 13 (=) ks cmsy10.329 @sf 13 r save [<000F0038006000E001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C003 8007001E00F8001E000700038001C001C001C001C001C001C001C001C001C001C001C001C001C0 01C001C000E000600038000F> 16 45 -3 11 23] 102 @pc restore cmr10.329 @sf 23 r m (0) s cmsy10.329 @sf save [ 16 45 -3 11 23] 103 @pc restore 35 r save [<00010000000003000000000300000000060000000006000000000C0000000018000000003FFFFF F8007FFFFFFC00C000000003800000000F000000003C00000000F8000000003E00000000070000 000001C000000000FFFFFFFC003FFFFFF80018000000000C000000000C00000000060000000003 00000000030000000001000000> 38 26 -3 2 45] 40 @pc restore 38 r save [<00000200000000030000000003000000000180000000018000000000C00000000060007FFFFFF0 00FFFFFFF8000000000C00000000070000000003C000000000F0000000007C00000001F0000000 03800000000E00FFFFFFFC007FFFFFF0000000006000000000C000000000C00000000180000000 03000000000300000000020000> 38 26 -3 2 45] 41 @pc restore cmr10.329 @sf 58 r m (rank) s cmex10.300 @sf 1121 2177 p save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pc restore 1154 2177 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 1200 2222 p m (A) s 1199 2277 p m (B) s cmex10.300 @sf 1256 2177 p save [ 12 124 0 122 24] 35 @pc restore 1280 2177 p save [ 21 124 -1 122 33] 33 @pc restore cmr10.329 @sf 1326 2249 p m (=) s cmmi10.329 @sf 13 r m (n:) s cmr10.329 @sf 1802 2249 p m (\(6\)) s 60 2381 p m (These) 17 (conditions) 19 (ensure) 17 (that) 17 (the) 17 (problem) 17 (LSE) 18 (has) 17 (a) 17 (unique) 18 (solution) 18 (whic) 0 (h) 17 (w) 0 (e) 16 (denote) 17 (b) 0 (y) ks cmmi10.329 @sf 60 2438 p m (x) s cmr8.300 @sf 86 2445 p m (e) s cmr10.329 @sf 104 2438 p m (.) s 131 2503 p m (Sev) 0 (eral) 17 (metho) 1 (ds) 19 (for) 17 (solving) 20 (the) 18 (problem) 19 (LSE) 19 (are) 18 (discussed) 20 (in) 19 (La) 0 (wson) 17 (and) 18 (Hanson[) 0 (8) ks 1847 2503 p m (,) s 60 2559 p m (Chaps.20-22],) 15 (V) -3 (an) 16 (Loan[) 0 (12) ks 597 2559 p m (].) 24 (F) -3 (or) 15 (large) 16 (sparse) 17 (matrices) 16 (case,) 17 (see) 17 (Barlo) 0 (w) ks cmti10.329 @sf 15 r m (et) 18 (al) ks cmr10.329 @sf 16 r m ([) 0 (1) ks 1647 2559 p m (].) 23 (The) 17 (QR) ks 60 2616 p m (st) 0 (yle) 13 (approac) 0 (h) 12 (is) 14 (one) 13 (of) 13 (the) 14 (most) 12 (common) 13 (approac) 0 (h.) 18 (No) 0 (w) 12 (this) 14 (approac) 0 (h) 12 (can) 14 (b) 1 (e) 14 (more) 13 (easily) ks 60 2672 p m (presen) 0 (ted) 15 (in) 16 (terms) 14 (of) 15 (the) 15 (GQR) 16 (factorization) 15 (of) ks cmmi10.329 @sf 15 r m (A) s cmr10.329 @sf 15 r m (and) s cmmi10.329 @sf 15 r m (B) s cmr10.329 @sf 2 r m (.) s @eop 8 @bop0 8 @bop1 cmsl10.329 @sf 60 -99 p m (The) 15 (Generalized) 17 (QR) 16 (Decomp) 1 (osition) ks cmr10.329 @sf 1059 r m (8) s 60 45 p m (the) 13 (factorizations,) 13 (the) 14 (orthogonal) 12 (matrix) 13 (can) 14 (b) 1 (e) 14 (reco) 0 (v) -1 (ered) 12 (from) 13 (the) 13 (elemen) 0 (ts) 13 (b) 1 (elo) 0 (w) 13 (\(ab) 1 (o) 0 (v) -1 (e\)) ks 60 102 p m (the) 15 (diagonal) 16 (with) 16 (another) 14 (one) 16 (dimensional) 17 (arra) 0 (y) -4 (.) ks 131 166 p m (T) -3 (urning) 14 (to) 15 (compute) 15 (GQR) 15 (factorization,) 15 (w) 0 (e) 13 (\014rst) 15 (presen) 0 (t) 14 (the) 15 (GQR) 15 (factorization) 15 (of) ks cmmi10.329 @sf 15 r m (n) s cmr10.329 @sf 15 r m (b) 0 (y) ks cmmi10.329 @sf 60 223 p m (m) s cmr10.329 @sf 16 r m (matrix) s cmmi10.329 @sf 17 r m (A) s cmr10.329 @sf 16 r m (and) s cmmi10.329 @sf 17 r m (n) s cmr10.329 @sf 17 r m (b) 0 (y) ks cmmi10.329 @sf 16 r m (m) s cmr10.329 @sf 16 r m (matrix) s cmmi10.329 @sf 16 r m (B) s cmr10.329 @sf 20 r m (with) s cmmi10.329 @sf 16 r m (n) s cmsy10.329 @sf 16 r save [ 26 36 -4 7 35] 21 @pc restore cmmi10.329 @sf 50 r m (m) s cmr10.329 @sf m (,) 17 (then) 16 (the) 17 (GR) 0 (Q) 16 (factorizations) 16 (for) 16 (the) 17 (case) ks cmmi10.329 @sf 60 279 p m (n) s cmsy10.329 @sf 13 r save [ 26 36 -4 7 35] 20 @pc restore cmmi10.329 @sf 48 r m (m) s cmr10.329 @sf 15 r m (and) 15 (GQR) 16 (factorization) 15 (with) 16 (column) 16 (piv) 0 (oting.) ks cmbx10.329 @sf 131 404 p save [ 35 31 -2 0 40] 65 @pc restore 40 r m (l) s save [<01FF000FFFE03F01F878003C78003CF0001EF0001EF0001E70003E3C007C1FFFFC07FFF80FFFF0 1FFF801C000018000018000009FC000FFF000F07801E03C03E03E03E03E03E03E03E03E03E03E0 1E03DE0F079E07FFFE01FC3C> 23 30 -1 10 26] 103 @pc restore 26 r m (orit) s save [ 24 32 -3 0 29] 104 @pc restore 29 r m (m) s 15 r save [ 17 29 -4 0 26] 49 @pc restore cmr10.329 @sf 42 r m (\(GQR) 15 (factorization,) ks cmmi10.329 @sf 15 r m (n) s cmsy10.329 @sf 12 r save [ 26 36 -4 7 35] 21 @pc restore cmmi10.329 @sf 48 r m (m) s cmr10.329 @sf m (\)) s 266 469 p m (1\).) 19 (QR) 16 (factoriztion) 15 (of) ks cmmi10.329 @sf 15 r m (A) s cmr10.329 @sf m (:) s cmmi10.329 @sf 20 r m (Q) s cmr8.300 @sf 819 454 p m (T) s cmmi10.329 @sf 846 469 p m (A) s cmr10.329 @sf 13 r m (=) s cmmi10.329 @sf 13 r m (R) s cmr10.329 @sf 15 r m (and) s cmmi10.329 @sf 15 r m (B) s cmr10.329 @sf 16 r m (=) s cmmi10.329 @sf 13 r m (Q) s cmr8.300 @sf 1213 454 p m (T) s cmmi10.329 @sf 1240 469 p m (B) s cmr10.329 @sf 2 r m (.) s 266 533 p m (2\).) 19 (R) 0 (Q) 15 (factorization) 15 (of) ks cmmi10.329 @sf 14 r m (B) s cmr10.329 @sf 2 r m (:) s cmmi10.329 @sf 21 r m (B) s 2 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr8.300 @sf 880 518 p m (T) s cmr10.329 @sf 921 533 p m (=) s cmmi10.329 @sf 13 r m (S) s cmr10.329 @sf 3 r m (.) s 131 658 p m (T) -3 (o) 12 (implemen) 0 (t) 14 (Algorithm) 14 (1,) 14 (w) 0 (e) 12 (note) 14 (that) 13 (the) 14 (blo) 1 (c) 0 (k) 13 (transformations) 13 (can) 14 (b) 1 (e) 14 (applied) 16 (to) ks cmmi10.329 @sf 13 r m (B) s cmr10.329 @sf 60 715 p m (at) 16 (the) 16 (same) 17 (time) 16 (while) ks cmmi10.329 @sf 18 r m (A) s cmr10.329 @sf 17 r m (is) 17 (reduced) 18 (to) 16 (upp) 1 (er) 17 (triangular) 17 (form) 15 (blo) 1 (c) 0 (k) 17 (b) 0 (y) 15 (blo) 1 (c) 0 (k.) 24 (A) 0 (t) 15 (the) 16 (end) ks 60 771 p m (of) 15 (step) 16 (1,) 15 (the) 15 (upp) 1 (er) 17 (diagonal) 16 (line) 17 (part) 15 (of) ks cmmi10.329 @sf 15 r m (A) s cmr10.329 @sf 16 r m (stores) 14 (the) 16 (factor) ks cmmi10.329 @sf 14 r m (R) s cmr10.329 @sf m (,) 16 (the) 15 (strictly) 16 (lo) 0 (w) 0 (er) 13 (diagonal) ks 60 828 p m (line) 17 (of) ks cmmi10.329 @sf 15 r m (A) s cmr10.329 @sf 15 r m (and) 16 (another) 15 (v) 0 (ector) 14 (stores) 14 (Householder) 17 (v) 0 (ectors) 13 (from) 15 (whic) 0 (h) 15 (the) 16 (orthogonal) 14 (matrix) ks cmmi10.329 @sf 60 884 p m (Q) s cmr10.329 @sf 16 r m (can) 16 (b) 1 (e) 17 (reco) 0 (v) 0 (ered) 14 (later) 17 (if) 16 (necessary) -3 (.) 23 (A) 0 (t) 14 (step) 16 (2,) 16 (w) 0 (e) 15 (just) 16 (need) 17 (to) 16 (implemen) 0 (t) 16 (the) 16 (blo) 1 (c) 0 (k) 16 (R) 0 (Q) ks 60 941 p m (factorization) 15 (on) 15 (up) 1 (dated) ks cmmi10.329 @sf 16 r m (B) s cmr10.329 @sf 2 r m (.) s 131 1005 p m (When) s cmmi10.329 @sf 16 r m (A) s cmr10.329 @sf 16 r m (is) s cmmi10.329 @sf 16 r m (n) s cmr10.329 @sf 17 r m (b) 0 (y) ks cmmi10.329 @sf 14 r m (m) s cmr10.329 @sf 16 r m (with) s cmmi10.329 @sf 17 r m (n) s cmsy10.329 @sf 14 r save [ 26 36 -4 7 35] 20 @pc restore cmmi10.329 @sf 49 r m (m) s cmr10.329 @sf m (,) s cmmi10.329 @sf 16 r m (B) s cmr10.329 @sf 18 r m (is) s cmmi10.329 @sf 17 r m (n) s cmr10.329 @sf 16 r m (b) 0 (y) ks cmmi10.329 @sf 15 r m (p) s cmr10.329 @sf 16 r m (matrix,) 15 (the) 16 (follo) 0 (wing) 16 (algorithm) 16 (computes) ks 60 1062 p m (the) 15 (GR) 0 (Q) 15 (factorization.) ks cmbx10.329 @sf 131 1186 p save [ 35 31 -2 0 40] 65 @pc restore 40 r m (l) s save [<01FF000FFFE03F01F878003C78003CF0001EF0001EF0001E70003E3C007C1FFFFC07FFF80FFFF0 1FFF801C000018000018000009FC000FFF000F07801E03C03E03E03E03E03E03E03E03E03E03E0 1E03DE0F079E07FFFE01FC3C> 23 30 -1 10 26] 103 @pc restore 26 r m (orit) s save [ 24 32 -3 0 29] 104 @pc restore 29 r m (m) s 15 r save [ 19 29 -3 0 26] 50 @pc restore cmr10.329 @sf 42 r m (\(GR) 0 (Q) 14 (factorization,) ks cmmi10.329 @sf 14 r m (n) s cmsy10.329 @sf 13 r save [ 26 36 -4 7 35] 20 @pc restore cmmi10.329 @sf 48 r m (m) s cmr10.329 @sf m (\)) s 266 1251 p m (1.\)) 19 (QR) 16 (factorization) 15 (of) ks cmmi10.329 @sf 15 r m (B) s cmr10.329 @sf 2 r m (:) s cmmi10.329 @sf 20 r m (Q) s cmr8.300 @sf 844 1236 p m (T) s cmmi10.329 @sf 872 1251 p m (B) s cmr10.329 @sf 15 r m (=) s cmmi10.329 @sf 13 r m (S) s cmr10.329 @sf 3 r m (,) 14 (and) ks cmmi10.329 @sf 16 r m (A) s cmr10.329 @sf 12 r m (=) s cmmi10.329 @sf 13 r m (Q) s cmr8.300 @sf 1246 1236 p m (T) s cmmi10.329 @sf 1274 1251 p m (A) s cmr10.329 @sf m (.) s 266 1316 p m (2.\)) 19 (R) 0 (Q) 15 (factorization) 15 (of) ks cmmi10.329 @sf 14 r m (A) s cmr10.329 @sf m (:) s cmmi10.329 @sf 20 r m (A) s cmr10.329 @sf 13 r m (=) s cmmi10.329 @sf 13 r m (R) s save [<07E000000C18000038040000300200007001000070008000F0004000F0004000F0002000F00020 00F0002000780010007800100078001000780010003C0008003C0008003C0008003C0008001E00 04001E0004001E0004001E0004000F0002000F0002000F0002000F000200078001000780010007 80010007C003C07FFC1FF8> 29 32 -4 1 31] 85 @pc restore cmr10.329 @sf 36 r m (.) s 131 1441 p m (The) 16 (remarks) 15 (for) 15 (algorithm) 16 (1) 16 (can) 16 (b) 1 (e) 17 (established) 18 (similarly) 17 (in) 17 (this) 17 (case.) 22 (Finally) -3 (,) 17 (to) 15 (treat) ks 60 1497 p m (with) 15 (ill-condi) 1 (tione) 1 (d) 16 (or) 14 (rank) 15 (de\014cien) 0 (t) 15 (cases,) 14 (w) 0 (e) 13 (can) 15 (use) 15 (the) 15 (GQR) 15 (factorization) 14 (with) 15 (column) ks 60 1554 p m (piv) 0 (oting.) ks cmbx10.329 @sf 131 1678 p save [ 35 31 -2 0 40] 65 @pc restore 40 r m (l) s save [<01FF000FFFE03F01F878003C78003CF0001EF0001EF0001E70003E3C007C1FFFFC07FFF80FFFF0 1FFF801C000018000018000009FC000FFF000F07801E03C03E03E03E03E03E03E03E03E03E03E0 1E03DE0F079E07FFFE01FC3C> 23 30 -1 10 26] 103 @pc restore 26 r m (orit) s save [ 24 32 -3 0 29] 104 @pc restore 29 r m (m) s 15 r save [<03FC001FFF803C0FC07807E0FC03F0FE03F0FE03F8FE03F87C03F83803F80003F80003F00003E0 0007C0000F8001FC0001FC00001F00000F80000FC01E0FC03F07E03F07E03F07E03F07E01E0FC0 0E0F8007FF0001FC00> 21 29 -2 0 26] 51 @pc restore cmr10.329 @sf 42 r m (\(GQR) 15 (factorization) 15 (with) 15 (piv) 0 (oting\)) ks 266 1743 p m (1\).) 19 (QR) 16 (factorization) 15 (with) 15 (piv) 0 (oting) 15 (of) ks cmmi10.329 @sf 15 r m (A) s cmr10.329 @sf m (:) s cmmi10.329 @sf 20 r m (Q) s cmr8.300 @sf 1122 1728 p m (T) s cmmi10.329 @sf 1149 1743 p m (AP) s cmr10.329 @sf 20 r m (=) s cmmi10.329 @sf 13 r m (R) s cmr10.329 @sf 15 r m (and) s cmmi10.329 @sf 15 r m (B) s cmr10.329 @sf 15 r m (=) s cmmi10.329 @sf 13 r m (Q) s cmr8.300 @sf 1551 1728 p m (T) s cmmi10.329 @sf 1579 1743 p m (B) s cmr10.329 @sf 2 r m (.) s 266 1808 p m (2\).) 19 (determine) 16 (the) 15 (rank) ks cmmi10.329 @sf 15 r m (q) s cmr10.329 @sf 17 r m (of) s cmmi10.329 @sf 15 r m (A) s cmr10.329 @sf m (.) s 266 1873 p m (3\).) 19 (if) 16 (\() ks cmmi10.329 @sf m (n) s cmsy10.329 @sf 12 r save [ 26 36 -4 7 35] 20 @pc restore cmmi10.329 @sf 48 r m (p) s cmr10.329 @sf m (\)) 15 (then) ks 386 1937 p m (R) 0 (Q) 14 (factorization) 15 (of) ks cmmi10.329 @sf 15 r m (B) s cmr10.329 @sf 2 r m (:) s cmmi10.329 @sf 21 r m (B) s 2 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr8.300 @sf 927 1922 p m (T) s cmr10.329 @sf 967 1937 p m (=) s cmmi10.329 @sf 13 r m (S) s cmr10.329 @sf 386 2002 p m (QR) 16 (factorization) 15 (with) 15 (piv) 0 (oting) 15 (of) ks cmmi10.329 @sf 15 r m (S) s cmr10.329 @sf 3 r m (\() s cmmi10.329 @sf m (q) s cmr10.329 @sf 11 r m (+) 10 (1) 13 (:) ks cmmi10.329 @sf 12 r m (n;) 8 (p) ks cmsy10.329 @sf 9 r m (\000) s cmmi10.329 @sf 11 r m (n) s cmr10.329 @sf 10 r m (+) s cmmi10.329 @sf 11 r m (q) s cmr10.329 @sf 12 r m (+) 10 (1) 13 (:) ks cmmi10.329 @sf 12 r m (p) s cmr10.329 @sf m (\)) s 326 2067 p m (else) s 386 2132 p m (if) 15 (\() ks cmmi10.329 @sf m (p) s cmsy10.329 @sf 13 r save [ 26 36 -4 7 35] 20 @pc restore cmmi10.329 @sf 48 r m (n) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (q) s cmr10.329 @sf 2 r m (\)) 15 (then) ks 446 2196 p m (QR) 16 (factorization) 15 (with) 15 (piv) 0 (oting) 15 (of) ks cmmi10.329 @sf 15 r m (B) s cmr10.329 @sf 2 r m (\() s cmmi10.329 @sf m (q) s cmr10.329 @sf 12 r m (+) 11 (1) 12 (:) ks cmmi10.329 @sf 12 r m (n;) s cmr10.329 @sf 8 r m (1) 12 (:) ks cmmi10.329 @sf 12 r m (p) s cmr10.329 @sf m (\).) s 386 2261 p m (else) s 446 2326 p m (R) 0 (Q) 14 (factorization) 15 (of) ks cmmi10.329 @sf 15 r m (B) s cmr10.329 @sf 2 r m (:) s cmmi10.329 @sf 21 r m (B) s 2 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr8.300 @sf 987 2311 p m (T) s cmr10.329 @sf 1027 2326 p m (=) s cmmi10.329 @sf 13 r m (S) s cmr10.329 @sf 3 r m (,) s 446 2391 p m (QR) 16 (factorization) 15 (with) 15 (piv) 0 (oting) 15 (of) ks cmmi10.329 @sf 15 r m (S) s cmr10.329 @sf 3 r m (\() s cmmi10.329 @sf m (q) s cmr10.329 @sf 11 r m (+) 10 (1) 13 (:) ks cmmi10.329 @sf 12 r m (n;) 8 (q) ks cmr10.329 @sf 11 r m (+) 11 (1) ks cmmi10.329 @sf m (;) 8 (p) ks cmr10.329 @sf m (\).) s 386 2455 p m (endif) s 326 2520 p m (endif) s 326 2585 p m (Up) 1 (date) 15 (the) ks cmmi10.329 @sf 16 r m (q) s cmr10.329 @sf 12 r m (+) 10 (1) 15 (to) ks cmmi10.329 @sf 15 r m (n) s cmr10.329 @sf 15 r m (columns) 16 (of) ks cmmi10.329 @sf 15 r m (Q) s cmr10.329 @sf 15 r m (corresp) 1 (onden) 0 (tly) -3 (.) ks @eop 7 @bop0 7 @bop1 cmsl10.329 @sf 60 -99 p m (The) 15 (Generalized) 17 (QR) 16 (Decomp) 1 (osition) ks cmr10.329 @sf 1059 r m (7) s 131 45 p m (If) s cmmi10.329 @sf 15 r m (p) s 13 r save [ 26 26 -4 2 35] 62 @pc restore 47 r m (n) s cmsy10.329 @sf 11 r m (\000) s cmmi10.329 @sf 10 r m (q) s cmr10.329 @sf 2 r m (,) 15 (b) 0 (y) 14 (the) 15 (R) 0 (Q) 15 (factorization) 15 (of) ks 943 35 p m (\026) s cmmi10.329 @sf 932 46 p m (B) s cmr10.329 @sf 984 45 p m (w) 0 (e) 14 (ha) 0 (v) -1 (e) ks 677 173 p m (\() s cmmi10.329 @sf m (Q) s cmr8.300 @sf 731 157 p m (T) s 731 183 p m (1) s cmmi10.329 @sf 759 173 p m (B) s cmr10.329 @sf 2 r m (\)) s cmmi10.329 @sf save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr10.329 @sf 49 r m (=) s cmex10.300 @sf 939 99 p save [ 12 124 -11 122 24] 34 @pc restore cmr10.329 @sf 992 134 p m (\026) s cmmi10.329 @sf 984 145 p m (S) s cmr8.300 @sf 1012 152 p m (11) s cmr10.329 @sf 992 189 p m (\026) s cmmi10.329 @sf 984 200 p m (S) s cmr8.300 @sf 1012 207 p m (21) s cmex10.300 @sf 1070 99 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 1103 145 p m (n) s cmsy10.329 @sf 11 r m (\000) s cmmi10.329 @sf 10 r m (p) s 1103 199 p m (p) s 1005 262 p m (p) s 1251 200 p m (:) s cmr10.329 @sf 60 354 p m (The) 18 (conclusion) 20 (for) 17 (this) 18 (case) 18 (follo) 0 (ws) 17 (up) 1 (on) 19 (the) 18 (QR) 19 (factorization) 17 (with) 19 (piv) 0 (oting) 17 (of) ks cmmi10.329 @sf 18 r m (n) s cmsy10.329 @sf 12 r m (\000) s cmmi10.329 @sf 12 r m (q) s cmr10.329 @sf 20 r m (b) 0 (y) ks cmmi10.329 @sf 60 410 p m (n) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 11 r m (q) s cmr10.329 @sf 17 r m (b) 1 (ottom) 14 (righ) 0 (t) 14 (corner) 15 (submatrix) 16 (of) ks cmmi10.329 @sf 14 r m (S) s cmr8.300 @sf 885 417 p m (21) s cmr10.329 @sf 923 410 p m (.) s 19 r save [<7FFFFF80FFFFFF80C0000180C0000180C0000180C0000180C0000180C0000180C0000180C00001 80C0000180C0000180C0000180C0000180C0000180C0000180C0000180C0000180C0000180C000 0180C0000180C0000180C0000180FFFFFF807FFFFF80> 25 25 -4 -3 34] 50 @pc restore cmr10.329 @sf 131 475 p m (W) -3 (e) 18 (note) 18 (that) 19 (in) 19 (this) 20 (case,) 19 (if) ks cmmi10.329 @sf 20 r m (B) s cmr10.329 @sf 21 r m (is) 20 (square) 18 (and) 20 (nonsingular,) 20 (then) 19 (the) 19 (QR) 20 (factorization) ks 60 532 p m (with) 16 (column) 16 (piv) 0 (oting) 14 (of) ks cmmi10.329 @sf 15 r m (B) s cmsy8.300 @sf 587 517 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 635 532 p m (A) s cmr10.329 @sf 15 r m (is) 16 (giv) 0 (en) 15 (b) 0 (y) ks cmmi10.329 @sf 670 658 p save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr8.300 @sf 706 640 p m (T) s cmr10.329 @sf 734 658 p m (\() s cmmi10.329 @sf m (B) s cmsy8.300 @sf 788 640 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 835 658 p m (A) s cmr10.329 @sf m (\)) s cmmi10.329 @sf m (P) s cmr10.329 @sf 19 r m (=) s cmmi10.329 @sf 13 r m (S) s cmsy8.300 @sf 1014 640 p m (\000) s cmr8.300 @sf m (1) s 1011 670 p m (11) s cmex10.300 @sf 1068 586 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 1113 631 p m (R) s cmr8.300 @sf 1148 638 p m (11) s cmr10.329 @sf 1138 686 p m (0) s cmex10.300 @sf 1206 586 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 1238 658 p m (:) s cmr10.329 @sf 60 784 p m (Hence) 16 (w) 0 (e) 14 (presen) 0 (t) ks cmbx10.329 @sf 131 908 p save [ 34 31 -2 0 40] 68 @pc restore 40 r m (e) s save [<3FF9FFC03FF9FFC007C03E0007C03E0007C03E0007C03E0007C03E0007C03E0007C03E0007C03E 0007C03E0007C03E0007C03E0007C03E0007C03E0007C03E0007C03E0007C03E00FFFFFE00FFFF FE0007C1FE0007C0000007C0000007C0000007C0380007C07C0007C07C0003E07C0001E07C0000 F81C00007FF800000FE000> 26 32 0 0 29] 12 @pc restore 29 r m (nition:) s cmr10.329 @sf 21 r m (F) -3 (or) ks cmmi10.329 @sf 13 r m (n) s cmr10.329 @sf 14 r m (b) 0 (y) ks cmmi10.329 @sf 14 r m (m) s cmr10.329 @sf 14 r m (matrix) s cmmi10.329 @sf 15 r m (A) s cmr10.329 @sf m (,) s cmmi10.329 @sf 14 r m (n) s cmr10.329 @sf 15 r m (b) 0 (y) ks cmmi10.329 @sf 13 r m (m) s cmr10.329 @sf 15 r m (matrix) s cmmi10.329 @sf 14 r m (B) s cmr10.329 @sf 2 r m (,) 15 (w) 0 (e) 13 (call) 16 (\(3\)) 14 (as) ks cmti10.329 @sf 14 r m (the) 16 (gener) -1 (ali) ks save [<80E00041F80063FC003E0C00100200080200040100020000010000008000004000002000001000 0008000004000802000C1F0007F18003E08001C040> 18 20 -3 0 19] 122 @pc restore 18 r m (e) -2 (d) ks 14 r save [<0000F0000001F8000003FC000003FE000003860000038300000101000001018001FD0080074380 800E41E0001C41700038413C0038411E0070200F00701C070070000380F00003C0F00001C0F000 01E0F00000E0F00000F0F00000F0780000787800007878000078780000783C0000783C0000381E 0000381E0000380F00003807000038078000780380007001C0007000E000E0003000E0001C01C0 000707000001FC00> 29 41 -6 9 35] 81 @pc restore 35 r m (R) s 60 965 p m (factori) s save [<80E00041F80063FC003E0C00100200080200040100020000010000008000004000002000001000 0008000004000802000C1F0007F18003E08001C040> 18 20 -3 0 19] 122 @pc restore 19 r m (ation) 16 (with) 17 (c) -1 (olumn) 15 (pi) ks save [<03C0000E30001C08001C04001C04001C02001C02001C01001C01001C01000E00800E00800E0080 8700804700C04301C04383C02307C03307800E0380> 18 20 -4 0 21] 118 @pc restore 21 r m (oting) s cmr10.329 @sf 15 r m (\(in) 16 (short) ks cmti10.329 @sf 14 r m (the) s 17 r save [<00FC0000038304000E00CC001C002E0018003E0038001E0070001E0070000F0070000F0070000F 00F0000F00F0000780F0000780F000FFF0F0000000780000007800000078000000780000003C00 00003C0000001E0000201E0000200E00003007000030038000300380003001C0003800E0007800 300078001C00980007030C0000FC04> 30 33 -6 1 35] 71 @pc restore 35 r save [<0000F0000001F8000003FC000003FE000003860000038300000101000001018001FD0080074380 800E41E0001C41700038413C0038411E0070200F00701C070070000380F00003C0F00001C0F000 01E0F00000E0F00000F0F00000F0780000787800007878000078780000783C0000783C0000381E 0000381E0000380F00003807000038078000780380007001C0007000E000E0003000E0001C01C0 000707000001FC00> 29 41 -6 9 35] 81 @pc restore 35 r m (R) 16 (with) 17 (pi) ks save [<03C0000E30001C08001C04001C04001C02001C02001C01001C01001C01000E00800E00800E0080 8700804700C04301C04383C02307C03307800E0380> 18 20 -4 0 21] 118 @pc restore 21 r m (oting) s cmr10.329 @sf m (\)) 14 (of) 15 (matrices) ks cmmi10.329 @sf 15 r m (A) s cmr10.329 @sf 16 r m (and) s cmmi10.329 @sf 15 r m (B) s cmr10.329 @sf 2 r m (.) s cmbx10.432 @sf 60 1115 p save [<007FFFF8007FFFF8007FFFF80000FE000000FE000000FE000000FE000000FE000000FE000000FE 000000FE00FFFFFFF8FFFFFFF8FFFFFFF8E0007E0070007E0038007E001C007E000E007E000E00 7E0007007E0003807E0001C07E0000E07E0000E07E0000707E0000387E00001C7E00000E7E0000 0E7E0000077E000003FE000001FE000000FE000000FE0000007E0000003E0000001E0000000E00> 29 39 -2 0 34] 52 @pc restore 163 1115 p save [ 22 41 -2 0 26] 73 @pc restore 26 r save [ 53 27 -3 0 60] 109 @pc restore 59 r save [ 33 39 -2 12 38] 112 @pc restore 38 r m (le) s -1 r save [ 53 27 -3 0 60] 109 @pc restore 58 r m (e) -1 (n) -2 (tat) ks save [ 15 43 -3 0 20] 105 @pc restore 19 r m (ons) s cmr10.329 @sf 60 1225 p m (In) 16 (this) 16 (section,) 15 (w) 0 (e) 15 (shall) 16 (discuss) 17 (the) 15 (algorithms) 15 (and) 16 (implemen) 0 (tation) 16 (details) 16 (of) 15 (GQR) 16 (factor-) ks 60 1282 p m (ization) 14 (and) 13 (its) 13 (v) -2 (arian) 0 (ts.) 17 (W) -3 (e) 12 (will) 15 (see) 13 (that) 13 (the) 13 (implemen) 0 (tations) 13 (of) 13 (all) 14 (these) 13 (factorizations) 13 (can) ks 60 1338 p m (b) 1 (e) 16 (easily) 16 (k) 0 (ept) 14 (in) 16 (the) 15 (blo) 1 (c) 0 (k) 15 (algorithm) 16 (fashion) 15 (as) 15 (QR) 16 (factorization) 15 (do) 1 (es.) ks 131 1403 p m (The) 14 (\\MA) -3 (TLAB") 13 (st) 0 (yle) 14 (notation) ks cmmi10.329 @sf 13 r m (A) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (i) s cmr10.329 @sf 12 r m (:) s cmmi10.329 @sf 13 r save [<3E0000638000F1C00078E000307000007000007000003800003800003800003800001C00001C00 001C00001C00000E00000E00000E00000E00000700000700000700020700010380010380008380 004380006300001E000000000000000000000000000000000000000000000001C00001E00001E0 0000C0> 19 40 1 9 19] 106 @pc restore 19 r m (;) 8 (p) ks cmr10.329 @sf 11 r m (:) s cmmi10.329 @sf 12 r m (q) s cmr10.329 @sf 2 r m (\)) 14 (is) 15 (used) 15 (in) 15 (this) 15 (section) 14 (to) 14 (sp) 1 (ecify) 15 (the) ks cmmi10.329 @sf 15 r m (i) s cmr10.329 @sf m (th) 14 (to) ks cmmi10.329 @sf 60 1459 p save [<3E0000638000F1C00078E000307000007000007000003800003800003800003800001C00001C00 001C00001C00000E00000E00000E00000E00000700000700000700020700010380010380008380 004380006300001E000000000000000000000000000000000000000000000001C00001E00001E0 0000C0> 19 40 1 9 19] 106 @pc restore cmr10.329 @sf 22 r m (th) 14 (ro) 0 (ws) 14 (and) ks cmmi10.329 @sf 15 r m (p) s cmr10.329 @sf m (th) 15 (to) ks cmmi10.329 @sf 14 r m (q) s cmr10.329 @sf 2 r m (th) 15 (columns) 16 (submatrix) 16 (of) 15 (matrix) ks cmmi10.329 @sf 14 r m (A) s cmr10.329 @sf m (.) s 131 1524 p m (As) 18 (w) 0 (as) 16 (men) 0 (tioned) 17 (in) 19 (section) 19 (2,) 18 (the) 18 (existence) 19 (pro) 1 (ofs) 18 (of) 17 (the) 18 (GQR) 19 (factorization) 18 (and) 18 (its) ks 60 1580 p m (v) -2 (arian) 0 (ts) 15 (are) 17 (constructiv) 0 (e.) 26 (They) 17 (strongly) 17 (dep) 1 (ends) 19 (on) 17 (the) 18 (regular) 17 (QR) 18 (factorization) 17 (and) 18 (its) ks 60 1637 p m (v) -2 (arian) 0 (ts.) 39 (A) 0 (t) 20 (the) 23 (b) 1 (eginning) 24 (of) 22 (this) 22 (note) 22 (w) 0 (e) 21 (brie\015y) 24 (review) 0 (ed) 22 (the) 22 (QR) 23 (factorizations) 22 (and) ks 60 1693 p m (its) 17 (v) -2 (arian) 0 (ts) -1 (,) 15 (the) 16 (corresp) 1 (onden) 0 (t) 16 (LAP) -3 (A) 0 (CK) 15 (subroutine) 17 (names) 16 (\(in) ks cmtt10.329 @sf 17 r m (typewriter) 23 (font) ks cmr10.329 @sf m (\)) 15 (and) 17 (its) ks 60 1750 p m (functions) 16 (are) 15 (listed) 16 (in) 16 (the) 16 (follo) 0 (wings:) ks cmtt10.329 @sf 174 1857 p m (SGEQRF) s cmr10.329 @sf m (:) 14 (QR) 16 (factorization) 15 (of) 14 (a) ks cmmi10.329 @sf 15 r m (n) s cmr10.329 @sf 16 r m (b) 0 (y) ks cmmi10.329 @sf 14 r m (m) s cmr10.329 @sf 15 r m (matrix.) s cmtt10.329 @sf 174 1931 p m (SGEQPF) s cmr10.329 @sf m (:) 14 (QR) 16 (factorization) 15 (of) 14 (a) ks cmmi10.329 @sf 15 r m (n) s cmr10.329 @sf 16 r m (b) 0 (y) ks cmmi10.329 @sf 14 r m (m) s cmr10.329 @sf 15 r m (matrix) 15 (with) 15 (column) 16 (piv) 0 (oting.) ks cmtt10.329 @sf 174 2006 p m (SGERQF) s cmr10.329 @sf m (:) 14 (R) 0 (Q) 14 (factorization) 15 (of) 15 (a) ks cmmi10.329 @sf 15 r m (n) s cmr10.329 @sf 15 r m (b) 0 (y) ks cmmi10.329 @sf 15 r m (m) s cmr10.329 @sf 15 r m (matrix.) s cmtt10.329 @sf 174 2080 p m (SGE) s save [<7FFFF0FFFFF07FFFF00E00700E00700E00700E00700E00700E00000E00000E00000E00000E0000 0E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00007FE000 FFE0007FE000> 20 28 -1 0 24] 76 @pc restore 24 r m (QF) s cmr10.329 @sf m (:) 14 (LQ) 15 (factorization) 16 (of) 14 (a) ks cmmi10.329 @sf 15 r m (n) s cmr10.329 @sf 16 r m (b) 0 (y) ks cmmi10.329 @sf 14 r m (m) s cmr10.329 @sf 15 r m (matrix.) s 131 2187 p m (All) 17 (these) 17 (subroutines) 17 (are) 16 (the) 17 (implemen) 0 (tations) 17 (of) 16 (the) 16 (blo) 1 (c) 0 (k) 16 (algorithms.) 24 (That) 16 (is) 17 (to) 16 (sa) 0 (y) -4 (,) ks 60 2244 p m (instead) 19 (of) 19 (traditional) 19 (algorithms) 19 (to) 18 (generate) 18 (and) 19 (apply) 20 (Householder) 19 (transformations) 18 (one) ks 60 2300 p m (b) 0 (y) 15 (one) 17 (\(BLAS) 17 (2) 16 (matrix-v) 0 (ector) 15 (op) 1 (erations\),) 16 (the) 17 (blo) 1 (c) 0 (k) 16 (algorithms) 17 (aggragate) 14 (a) 17 (series) 17 (\(sa) 0 (y) 14 (a) ks 60 2357 p m (blo) 1 (c) 0 (k) 19 (with) 19 (size) ks cmmi10.329 @sf 20 r m (b) s cmr10.329 @sf m (\)) 18 (of) 19 (Householder) 20 (transformations,) 18 (represen) 0 (t) 18 (in) 20 (a) 19 (blo) 1 (c) 0 (k) 19 (matrix) 18 (form) 19 (and) ks 60 2413 p m (apply) 15 (them) 15 (to) 14 (reduce) 15 (a) 14 (blo) 1 (c) 0 (k) 14 (at) 14 (the) 15 (same) 14 (time) 15 (\(BLAS) 15 (3) 14 (matrix-matrix) 14 (op) 1 (erations\).) 20 (There) ks 60 2469 p m (is) 16 (a) 15 (common) 14 (parameters) 15 (called) 16 (blo) 1 (c) 0 (ksize) ks cmtt10.329 @sf 16 r save [<7F03C0FF87C07F07C01C0DC01C0DC01C0DC01C1DC01C19C01C19C01C39C01C39C01C39C01C31C0 1C71C01C71C01C61C01CE1C01CE1C01CE1C01CC1C01CC1C01DC1C01D81C01D81C01D81C07F07F0 FF0FF87E07F0> 21 28 -1 0 24] 78 @pc restore 24 r m (B) s cmr10.329 @sf 15 r m (of) 15 (these) 15 (subroutines) 16 (that) 15 (allo) 0 (ws) 14 (user) 15 (to) 15 (c) 0 (hoice) ks 60 2526 p m (to) 15 (\014nd) 16 (the) 15 (b) 1 (est) 16 (blo) 1 (c) 0 (ksize) 16 (one) 16 (their) 16 (mac) 0 (hines.) 20 (In) 16 (particularly) -3 (,) 16 (if) 16 (blo) 1 (c) 0 (ksize) 16 (is) 16 (one,) 15 (then) 16 (they) ks 60 2582 p m (are) 15 (just) 15 (traditional) 16 (QR) 16 (factorizations) 15 (and) 15 (its) 15 (v) -2 (arian) 0 (ts.) ks 131 2647 p m (T) -3 (o) 16 (call) 19 (this) 18 (routine,) 19 (the) 18 (input) 19 (arra) 0 (y) ks cmtt10.329 @sf 15 r m (A) s cmr10.329 @sf 18 r m (con) 0 (tains) 17 (the) ks cmmi10.329 @sf 18 r m (n) s cmr10.329 @sf 18 r m (b) 0 (y) ks cmmi10.329 @sf 17 r m (m) s cmr10.329 @sf 18 r m (matrix.) 27 (On) 19 (the) 18 (return) 17 (of) ks 60 2704 p m (these) 19 (subroutines,) 20 (the) 18 (upp) 1 (er) 20 (\(lo) 0 (w) -1 (er\)) 17 (triangle) 19 (of) 18 (the) 19 (arra) 0 (y) 16 (con) 0 (tains) 18 (the) 19 (triangular) 18 (part) 18 (of) ks @eop 6 @bop0 cmti10.329 @sf [ 5 5 -5 0 14] 46 @dc cmr6.300 @sf [ 9 16 -2 0 15] 49 @dc 1.000000 /cmsy9.300 @newfont cmsy9.300 @sf [ 23 2 -3 -8 30] 0 @dc 1.000000 /cmr9.300 @newfont cmr9.300 @sf [<8040202010101070F0F060> 4 11 -3 7 11] 44 @dc 6 @bop1 cmsl10.329 @sf 60 -99 p m (The) 15 (Generalized) 17 (QR) 16 (Decomp) 1 (osition) ks cmr10.329 @sf 1059 r m (6) s cmti10.329 @sf 60 45 p m (wher) -1 (e) ks cmmi10.329 @sf 19 r m (R) s cmr8.300 @sf 227 52 p m (11) s cmti10.329 @sf 284 45 p m (and) s cmmi10.329 @sf 20 r m (S) s cmr8.300 @sf 404 52 p m (22) s cmti10.329 @sf 441 45 p m (,) 21 (if) 20 (which) 21 (exists,) 20 (ar) -1 (e) 19 (ful) 2 (l) 20 (r) -1 (ow) 19 (r) -1 (an) ks save [<601E00E0310070310070708070708070708038384038700038700038E0001FC0001E00001D0000 1C80000E40C00E21E00E11E00E08E00704200703C0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 19 32 -3 0 21] 107 @pc restore 40 r m (upp) -1 (er) 19 (tr) -1 (ap) -1 (e) ks save [<80E00041F80063FC003E0C00100200080200040100020000010000008000004000002000001000 0008000004000802000C1F0007F18003E08001C040> 18 20 -3 0 19] 122 @pc restore 19 r m (oidal) 18 (matric) -1 (es.) ks cmmi10.329 @sf 31 r m (q) s cmti10.329 @sf 22 r m (b) s save [<3E0000438000C0C000E06000F07000F03800003800001C00001C0007DC000C3C001C1E00180E00 180E001C0E001C07001C07001C07001C07000E03800E03800E03808703804701C04301C04381C0 2301C03300E00E00C0> 19 29 -4 9 22] 121 @pc restore cmmi10.329 @sf 42 r m (q) s cmti10.329 @sf 60 102 p m (matrix) s cmmi10.329 @sf 17 r m (S) s cmr8.300 @sf 234 109 p m (11) s cmti10.329 @sf 287 102 p m (is) 16 (upp) -1 (er) 16 (triangular.) 21 (A) 0 (nd) 15 (if) ks cmmi10.329 @sf 16 r m (n) s 13 r save [ 26 26 -4 2 35] 62 @pc restore 48 r m (p) s cmti10.329 @sf m (,) s cmmi10.329 @sf 233 260 p m (R) s cmr10.329 @sf 13 r m (=) s cmex10.300 @sf 358 162 p save [ 14 74 -13 73 28] 50 @pc restore 358 235 p m (6) s 358 262 p save [ 14 74 -13 72 28] 52 @pc restore cmmi10.329 @sf 406 202 p m (R) s cmr8.300 @sf 441 209 p m (11) s cmmi10.329 @sf 520 202 p m (R) s cmr8.300 @sf 555 209 p m (12) s cmr10.329 @sf 431 259 p m (0) s 544 259 p m (0) s 431 315 p m (0) s 544 315 p m (0) s cmex10.300 @sf 612 162 p save [<001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C00 1C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C 001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C00 1C001C001C001C001C001C001C001C001C001C001C001C001CFFFCFFFCFFFC> 14 74 0 73 28] 51 @pc restore 612 235 p m (7) s 612 262 p save [ 14 74 0 72 28] 53 @pc restore cmmi10.329 @sf 649 202 p m (q) s 649 259 p save [<600F00E01880701880703840703840703840381C203838003838003870001FC0001E00001D0000 1C80000E40600E20F00E10F00E08700706100701E0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 20 32 -2 0 24] 107 @pc restore 649 315 p m (n) s cmsy10.329 @sf 11 r m (\000) s cmmi10.329 @sf 10 r m (q) s cmsy10.329 @sf 12 r m (\000) s cmmi10.329 @sf 10 r save [<600F00E01880701880703840703840703840381C203838003838003870001FC0001E00001D0000 1C80000E40600E20F00E10F00E08700706100701E0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 20 32 -2 0 24] 107 @pc restore 408 374 p m (q) s 472 374 p m (m) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (q) s 876 287 p m (;) s 968 260 p m (S) s cmr10.329 @sf 15 r m (=) s cmex10.300 @sf 1139 162 p save [ 14 74 -13 73 28] 50 @pc restore 1139 235 p m (6) s 1139 262 p save [ 14 74 -13 72 28] 52 @pc restore cmmi10.329 @sf 1187 202 p m (S) s cmr8.300 @sf 1215 209 p m (11) s cmmi10.329 @sf 1294 202 p m (S) s cmr8.300 @sf 1322 209 p m (12) s cmr10.329 @sf 1208 259 p m (0) s cmmi10.329 @sf 1294 259 p m (S) s cmr8.300 @sf 1322 266 p m (22) s cmr10.329 @sf 1208 315 p m (0) s 1315 315 p m (0) s cmex10.300 @sf 1380 162 p save [<001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C00 1C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C 001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C00 1C001C001C001C001C001C001C001C001C001C001C001C001CFFFCFFFCFFFC> 14 74 0 73 28] 51 @pc restore 1380 235 p m (7) s 1380 262 p save [ 14 74 0 72 28] 53 @pc restore cmmi10.329 @sf 1468 202 p m (q) s 1468 259 p save [<600F00E01880701880703840703840703840381C203838003838003870001FC0001E00001D0000 1C80000E40600E20F00E10F00E08700706100701E0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 20 32 -2 0 24] 107 @pc restore 1468 315 p m (n) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 11 r m (q) s cmsy10.329 @sf 12 r m (\000) s cmmi10.329 @sf 10 r save [<600F00E01880701880703840703840703840381C203838003838003870001FC0001E00001D0000 1C80000E40600E20F00E10F00E08700706100701E0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 20 32 -2 0 24] 107 @pc restore 1108 374 p m (p) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 11 r m (n) s cmr10.329 @sf 10 r m (+) s cmmi10.329 @sf 11 r m (q) s 1333 374 p m (n) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 11 r m (q) s 1695 287 p m (;) s cmti10.329 @sf 60 472 p m (wher) -1 (e) ks cmmi10.329 @sf 16 r m (q) s cmti10.329 @sf 19 r m (b) s save [<3E0000438000C0C000E06000F07000F03800003800001C00001C0007DC000C3C001C1E00180E00 180E001C0E001C07001C07001C07001C07000E03800E03800E03808703804701C04301C04381C0 2301C03300E00E00C0> 19 29 -4 9 22] 121 @pc restore cmmi10.329 @sf 39 r m (q) s cmti10.329 @sf 20 r m (matrix) s cmmi10.329 @sf 17 r m (R) s cmr8.300 @sf 509 479 p m (11) s cmti10.329 @sf 563 472 p m (ar) -1 (e) 17 (nonsingular) 15 (and) 18 (upp) -1 (er) 16 (triangular,) 18 (and) ks cmmi10.329 @sf 17 r save [<600F00E01880701880703840703840703840381C203838003838003870001FC0001E00001D0000 1C80000E40600E20F00E10F00E08700706100701E0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 20 32 -2 0 24] 107 @pc restore cmti10.329 @sf 43 r m (b) s save [<3E0000438000C0C000E06000F07000F03800003800001C00001C0007DC000C3C001C1E00180E00 180E001C0E001C07001C07001C07001C07000E03800E03800E03808703804701C04301C04381C0 2301C03300E00E00C0> 19 29 -4 9 22] 121 @pc restore cmmi10.329 @sf 39 r m (n) s cmsy10.329 @sf 11 r m (\000) s cmmi10.329 @sf 11 r m (q) s cmti10.329 @sf 19 r m (matrix) s cmmi10.329 @sf 18 r m (S) s cmr8.300 @sf 1823 479 p m (22) s cmti10.329 @sf 60 529 p m (is) 16 (ful) 2 (l) 16 (r) -1 (ow) 15 (r) -1 (an) ks save [<601E00E0310070310070708070708070708038384038700038700038E0001FC0001E00001D0000 1C80000E40C00E21E00E11E00E08E00704200703C0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 19 32 -3 0 21] 107 @pc restore 36 r m (upp) -1 (er) 16 (tr) -1 (ap) -1 (e) ks save [<80E00041F80063FC003E0C00100200080200040100020000010000008000004000002000001000 0008000004000802000C1F0007F18003E08001C040> 18 20 -3 0 19] 122 @pc restore 19 r m (oidal) s cmr8.300 @sf 716 514 p m (1) s cmti10.329 @sf 734 529 p m (.) s 131 654 p save [ 30 31 -3 0 31] 80 @pc restore 31 r m (r) -1 (o) -2 (of) ks cmr10.329 @sf 14 r m (:) 21 (The) 16 (pro) 1 (of) 15 (is) 17 (also) 15 (constructiv) 0 (e.) 21 (By) 16 (the) 16 (QR) 16 (factorization) 16 (with) 16 (piv) 0 (oting) 15 (of) ks cmmi10.329 @sf 16 r m (A) s cmr10.329 @sf m (,) 15 (w) 0 (e) ks 60 710 p m (ha) 0 (v) -1 (e) ks cmmi10.329 @sf 637 789 p m (Q) s cmr8.300 @sf 673 773 p m (T) s 673 799 p m (1) s cmmi10.329 @sf 701 789 p m (AP) s cmr10.329 @sf 19 r m (=) s cmex10.300 @sf 860 716 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 905 762 p m (R) s cmr8.300 @sf 940 768 p m (11) s cmmi10.329 @sf 1018 762 p m (R) s cmr8.300 @sf 1053 768 p m (12) s cmr10.329 @sf 930 816 p m (0) s 1043 816 p m (0) s cmex10.300 @sf 1111 716 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 1144 762 p m (q) s 1144 816 p m (n) s cmsy10.329 @sf 11 r m (\000) s cmmi10.329 @sf 10 r m (q) s 907 878 p m (q) s 971 878 p m (m) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (q) s 1291 816 p m (:) s cmr10.329 @sf 60 961 p m (where) s cmmi10.329 @sf 15 r m (q) s cmr10.329 @sf 15 r m (=) 13 (rank) ks 364 961 p m (\() s cmmi10.329 @sf m (A) s cmr10.329 @sf m (\).) 19 (If) ks cmmi10.329 @sf 15 r m (n) s cmsy10.329 @sf 13 r save [ 26 36 -4 7 35] 20 @pc restore cmmi10.329 @sf 48 r m (p) s cmr10.329 @sf m (,) 15 (let) ks 578 1097 p m (\() s cmmi10.329 @sf m (Q) s cmr8.300 @sf 632 1081 p m (T) s 632 1107 p m (1) s cmmi10.329 @sf 660 1097 p m (B) s cmr10.329 @sf 2 r m (\)) s cmmi10.329 @sf save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr8.300 @sf 741 1104 p m (1) s cmr10.329 @sf 773 1097 p m (=) s cmex10.300 @sf 865 1023 p save [ 12 124 -11 122 24] 34 @pc restore cmr10.329 @sf 910 1069 p m (0) s cmmi10.329 @sf 974 1069 p m (S) s cmr8.300 @sf 1002 1076 p m (11) s cmr10.329 @sf 1089 1058 p m (\026) s cmmi10.329 @sf 1081 1069 p m (S) s cmr8.300 @sf 1109 1076 p m (12) s cmr10.329 @sf 910 1124 p m (0) s 996 1124 p m (0) s 1089 1114 p m (\026) s cmmi10.329 @sf 1081 1125 p m (S) s cmr8.300 @sf 1109 1132 p m (22) s cmex10.300 @sf 1167 1023 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 1216 1069 p m (q) s 1216 1124 p m (n) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 11 r m (q) s 871 1186 p m (p) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (n) s 1018 1186 p m (q) s 1081 1186 p m (n) s cmsy10.329 @sf 11 r m (\000) s cmmi10.329 @sf 10 r m (q) s cmr10.329 @sf 60 1292 p m (b) 1 (e) 19 (the) 19 (R) 0 (Q) 18 (factorization) 19 (of) 18 (matrix) ks cmmi10.329 @sf 18 r m (Q) s cmr8.300 @sf 803 1277 p m (T) s 803 1303 p m (1) s cmmi10.329 @sf 831 1292 p m (B) s cmr10.329 @sf 2 r m (.) 31 (Then) 19 (b) 0 (y) 17 (the) 19 (QR) 20 (factorization) 18 (with) 19 (piv) 0 (oting) 18 (of) ks 60 1348 p m (submatrix) s 284 1338 p m (\026) s cmmi10.329 @sf 276 1349 p m (S) s cmr8.300 @sf 304 1356 p m (22) s cmr10.329 @sf 342 1348 p m (,) 14 (w) 0 (e) 14 (ha) 0 (v) 0 (e) ks cmmi10.329 @sf 635 1482 p m (Q) s cmr8.300 @sf 671 1466 p m (T) s 671 1492 p m (2) s cmr10.329 @sf 706 1471 p m (\026) s cmmi10.329 @sf 698 1482 p m (S) s cmr8.300 @sf 726 1489 p m (22) s cmmi10.329 @sf 764 1482 p m (P) s cmr8.300 @sf 793 1489 p m (2) s cmr10.329 @sf 825 1482 p m (=) s cmex10.300 @sf 902 1409 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 947 1454 p m (S) s cmr8.300 @sf 975 1461 p m (22) s cmr10.329 @sf 968 1509 p m (0) s cmex10.300 @sf 1033 1409 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 1066 1454 p save [<600F00E01880701880703840703840703840381C203838003838003870001FC0001E00001D0000 1C80000E40600E20F00E10F00E08700706100701E0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 20 32 -2 0 24] 107 @pc restore 1066 1509 p m (n) s cmsy10.329 @sf 11 r m (\000) s cmmi10.329 @sf 10 r m (q) s cmsy10.329 @sf 12 r m (\000) s cmmi10.329 @sf 11 r save [<600F00E01880701880703840703840703840381C203838003838003870001FC0001E00001D0000 1C80000E40600E20F00E10F00E08700706100701E0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 20 32 -2 0 24] 107 @pc restore 927 1571 p m (n) s cmsy10.329 @sf 11 r m (\000) s cmmi10.329 @sf 10 r m (q) s 1293 1509 p m (:) s cmr10.329 @sf 60 1711 p m (The) 15 (result) 16 (for) 15 (this) 15 (case) 15 (follo) 0 (ws) 15 (b) 0 (y) 14 (setting) ks cmmi10.329 @sf 15 r m (Q) s cmr10.329 @sf 13 r m (=) s cmmi10.329 @sf 13 r m (Q) s cmr8.300 @sf 1029 1718 p m (1) s cmex10.300 @sf 1056 1639 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 1101 1684 p m (I) s cmr10.329 @sf 1182 1684 p m (0) s 1101 1739 p m (0) s cmmi10.329 @sf 1166 1739 p m (Q) s cmr8.300 @sf 1202 1746 p m (2) s cmex10.300 @sf 1242 1639 p save [ 12 124 0 122 24] 35 @pc restore cmr10.329 @sf 1267 1711 p m (,) s cmmi10.329 @sf 14 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr10.329 @sf 50 r m (=) s cmmi10.329 @sf 12 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr8.300 @sf 1418 1718 p m (1) s cmex10.300 @sf 1445 1639 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 1490 1684 p m (I) s cmr10.329 @sf 1568 1684 p m (0) s 1491 1739 p m (0) s cmmi10.329 @sf 1555 1739 p m (P) s cmr8.300 @sf 1584 1746 p m (2) s cmex10.300 @sf 1625 1639 p save [ 12 124 0 122 24] 35 @pc restore cmr10.329 @sf 1649 1711 p m (.) s 131 1814 p m (If) s cmmi10.329 @sf 15 r m (n) s 13 r save [ 26 26 -4 2 35] 62 @pc restore 48 r m (p) s cmr10.329 @sf m (,) 15 (let) ks cmmi10.329 @sf 15 r m (Q) s cmr8.300 @sf 416 1799 p m (T) s 416 1825 p m (1) s cmr10.329 @sf 459 1814 p m (prem) 0 (ultiply) 16 (on) ks cmmi10.329 @sf 15 r m (B) s cmr10.329 @sf 2 r m (,) 16 (denote) 15 (as) ks cmmi10.329 @sf 665 1950 p m (Q) s cmr8.300 @sf 701 1934 p m (T) s 701 1960 p m (1) s cmmi10.329 @sf 729 1950 p m (B) s cmr10.329 @sf 15 r m (=) s 837 1939 p m (\026) s cmmi10.329 @sf 826 1950 p m (B) s cmr10.329 @sf 875 1950 p m (=) s cmex10.300 @sf 952 1877 p save [ 12 124 -11 122 24] 34 @pc restore cmr10.329 @sf 1005 1911 p m (\026) s cmmi10.329 @sf 997 1922 p m (S) s cmr8.300 @sf 1025 1929 p m (11) s cmr10.329 @sf 1005 1967 p m (\026) s cmmi10.329 @sf 997 1978 p m (S) s cmr8.300 @sf 1025 1985 p m (21) s cmex10.300 @sf 1083 1877 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 1117 1923 p m (q) s 1117 1977 p m (n) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (q) s 1018 2039 p m (p) s 1263 1977 p m (:) s cmr10.329 @sf 60 2143 p m (if) s cmmi10.329 @sf 16 r m (p) s cmsy10.329 @sf 12 r save [ 26 36 -4 7 35] 20 @pc restore cmmi10.329 @sf 48 r m (n) s cmsy10.329 @sf 11 r m (\000) s cmmi10.329 @sf 10 r m (q) s cmr10.329 @sf 2 r m (,) 15 (then) 15 (b) 0 (y) 14 (the) 16 (QR) 16 (factorization) 15 (with) 15 (piv) 0 (oting) 15 (of) ks 1250 2133 p m (\026) s cmmi10.329 @sf 1243 2144 p m (S) s cmr8.300 @sf 1271 2151 p m (21) s cmr10.329 @sf 1308 2143 p m (,) 15 (w) 0 (e) 14 (ha) 0 (v) -1 (e) ks cmmi10.329 @sf 641 2277 p m (Q) s cmr8.300 @sf 677 2261 p m (T) s 677 2287 p m (2) s cmr10.329 @sf 712 2266 p m (\026) s cmmi10.329 @sf 705 2277 p m (S) s cmr8.300 @sf 733 2284 p m (21) s cmmi10.329 @sf 770 2277 p m (P) s cmr8.300 @sf 799 2284 p m (2) s cmr10.329 @sf 831 2277 p m (=) s cmex10.300 @sf 908 2204 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 953 2249 p m (S) s cmr8.300 @sf 981 2256 p m (21) s cmr10.329 @sf 974 2304 p m (0) s cmex10.300 @sf 1039 2204 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 1073 2249 p save [<600F00E01880701880703840703840703840381C203838003838003870001FC0001E00001D0000 1C80000E40600E20F00E10F00E08700706100701E0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 20 32 -2 0 24] 107 @pc restore 1073 2304 p m (n) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (q) s cmsy10.329 @sf 13 r m (\000) s cmmi10.329 @sf 10 r save [<600F00E01880701880703840703840703840381C203838003838003870001FC0001E00001D0000 1C80000E40600E20F00E10F00E08700706100701E0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 20 32 -2 0 24] 107 @pc restore 974 2366 p m (p) s cmr10.329 @sf 60 2470 p m (where) s cmmi10.329 @sf 15 r save [<600F00E01880701880703840703840703840381C203838003838003870001FC0001E00001D0000 1C80000E40600E20F00E10F00E08700706100701E0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 20 32 -2 0 24] 107 @pc restore cmr10.329 @sf 38 r m (=) 13 (rank) ks 367 2470 p m (\() s 392 2460 p m (\026) s cmmi10.329 @sf 385 2471 p m (S) s cmr8.300 @sf 413 2478 p m (21) s cmr10.329 @sf 450 2470 p m (\).) 19 (The) 16 (desired) 16 (factorization) 15 (forms) 15 (are) 14 (obtained) 16 (b) 0 (y) 14 (setting) ks cmmi10.329 @sf 60 2559 p m (Q) s cmr10.329 @sf 13 r m (=) s cmmi10.329 @sf 13 r m (Q) s cmr8.300 @sf 193 2566 p m (1) s cmex10.300 @sf 220 2487 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 265 2532 p m (I) s cmr10.329 @sf 346 2532 p m (0) s 265 2587 p m (0) s cmmi10.329 @sf 330 2587 p m (Q) s cmr8.300 @sf 366 2594 p m (2) s cmex10.300 @sf 406 2487 p save [ 12 124 0 122 24] 35 @pc restore cmr10.329 @sf 446 2559 p m (and) s cmmi10.329 @sf 15 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr10.329 @sf 49 r m (=) s cmmi10.329 @sf 13 r m (P) s cmr8.300 @sf 660 2566 p m (2) s cmr10.329 @sf 680 2559 p m (.) s 60 2641 p 720 2 ru cmr6.300 @sf 112 2669 p m (1) s cmr9.300 @sf 129 2684 p save [ 9 26 0 0 10] 105 @pc restore 10 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFC00E000E000E000E 000E000E000E100738031801F0> 13 26 0 0 12] 102 @pc restore 25 r save [ 18 23 1 7 19] 112 @pc restore 30 r save [<00000E00003C0000F00003C0000F00003C0000F00003C0000F00003C0000F00000F000003C0000 0F000003C00000F000003C00000F000003C00000F000003C00000E> 23 22 -3 2 30] 60 @pc restore 41 r save [<300E00701900383880383840381C40381C401C1C001C0E001C0E001C0E008E07008E07008E0700 8F07004CC600383C00> 18 16 -2 0 23] 110 @pc restore cmsy9.300 @sf 31 r m (\000) s 9 r save [<3FE0038003800380038001C001C03DC063C0E1E0C0E0C0E0C0E0E070E070E070E0707038303838 3818380C5C0384> 14 23 -2 7 17] 113 @pc restore cmr9.300 @sf 18 r m (,) s 13 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [ 18 26 -1 0 21] 104 @pc restore 21 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 18 16 -1 0 21] 110 @pc restore 34 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 15 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 28 r save [ 18 23 1 7 19] 112 @pc restore cmsy9.300 @sf 28 r m (\000) s 8 r save [<300E00701900383880383840381C40381C401C1C001C0E001C0E001C0E008E07008E07008E0700 8F07004CC600383C00> 18 16 -2 0 23] 110 @pc restore cmr9.300 @sf 32 r save [<000C0000000C0000000C0000000C0000000C0000000C0000000C0000000C0000000C0000000C00 00000C0000000C0000FFFFFF80FFFFFF80000C0000000C0000000C0000000C0000000C0000000C 0000000C0000000C0000000C0000000C0000000C0000000C0000> 25 26 -2 4 30] 43 @pc restore 39 r save [<3FE0038003800380038001C001C03DC063C0E1E0C0E0C0E0C0E0E070E070E070E0707038303838 3818380C5C0384> 14 23 -2 7 17] 113 @pc restore cmr9.300 @sf 31 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [<007FC0000E00000E00000E00000E00000E00000E0007CE001C2E00381E00700E00700E00E00E00 E00E00E00E00E00E00E00E00E00E00700E00300E00381E000C260003C200> 18 23 -1 7 20] 113 @pc restore 20 r save [<07CFC00C2E001C1E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E00 1C0E001C0E00FC7E00> 18 16 -1 0 21] 117 @pc restore 21 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [ 9 26 0 0 10] 108 @pc restore 24 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 32 r save [ 13 16 -1 0 17] 122 @pc restore 17 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r m (,) s 13 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 15 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 28 r save [<300E00701900383880383840381C40381C401C1C001C0E001C0E001C0E008E07008E07008E0700 8F07004CC600383C00> 18 16 -2 0 23] 110 @pc restore cmsy9.300 @sf 32 r m (\000) s 8 r save [<3FE0038003800380038001C001C03DC063C0E1E0C0E0C0E0C0E0E070E070E070E0707038303838 3818380C5C0384> 14 23 -2 7 17] 113 @pc restore cmr9.300 @sf 31 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [<007FC0000E00000E00000E00000E00000E00000E0007CE001C2E00381E00700E00700E00E00E00 E00E00E00E00E00E00E00E00E00E00700E00300E00381E000C260003C200> 18 23 -1 7 20] 113 @pc restore 20 r save [<07CFC00C2E001C1E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E00 1C0E001C0E00FC7E00> 18 16 -1 0 21] 117 @pc restore 21 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [ 9 26 0 0 10] 108 @pc restore 25 r save [ 18 23 1 7 19] 112 @pc restore cmr9.300 @sf 32 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [ 18 16 -1 0 21] 110 @pc restore 34 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [ 18 26 -1 0 21] 104 @pc restore 21 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 31 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFC00E000E000E000E 000E000E000E100738031801F0> 13 26 0 0 12] 102 @pc restore 12 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [<07E00C18380830047000E000E000E000E000E000E00070003008381C0C1C07F8> 14 16 -1 0 17] 99 @pc restore 17 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [ 13 16 -1 0 17] 122 @pc restore 17 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [ 18 16 -1 0 21] 110 @pc restore 36 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFC00E000E000E000E 000E000E000E100738031801F0> 13 26 0 0 12] 102 @pc restore 12 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [ 29 16 -1 0 32] 109 @pc restore 44 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFC00E000E000E000E 000E000E000E100738031801F0> 13 26 0 0 12] 102 @pc restore 25 r save [<83F000CC0C007006006003006001806001802000C02000C00000C00001C00001C00007C0007F80 01FF0003FC0007C0000700000600000600100600100600100300100100380080380060D8001F08> 21 26 -2 0 23] 83 @pc restore cmr9.300 @sf 25 r save [<60F0F060> 4 4 -3 0 11] 46 @pc restore @eop 5 @bop0 5 @bop1 cmsl10.329 @sf 60 -99 p m (The) 15 (Generalized) 17 (QR) 16 (Decomp) 1 (osition) ks cmr10.329 @sf 1059 r m (5) s cmti10.329 @sf 60 45 p m (assumes) 16 (one) 16 (of) 16 (the) 17 (fol) 2 (lowing) 15 (forms) ks 60 102 p m (if) s cmmi10.329 @sf 16 r m (n) s cmsy10.329 @sf 13 r save [ 26 36 -4 7 35] 20 @pc restore cmmi10.329 @sf 48 r m (p) s 508 165 p m (R) s cmr10.329 @sf 12 r m (=) s cmex10.300 @sf 640 116 p m (h) s cmr10.329 @sf 681 165 p m (0) s cmmi10.329 @sf 745 165 p m (R) s cmr8.300 @sf 780 172 p m (11) s cmex10.300 @sf 838 116 p m (i) s cmmi10.329 @sf 869 165 p m (n) s 653 229 p m (m) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (n) s 817 229 p m (n) s 917 192 p m (;) s 996 165 p m (S) s cmr10.329 @sf 15 r m (=) s cmex10.300 @sf 1116 116 p m (h) s cmmi10.329 @sf 1156 165 p m (S) s cmr8.300 @sf 1184 172 p m (11) s cmmi10.329 @sf 1263 165 p m (S) s cmr8.300 @sf 1291 172 p m (12) s cmex10.300 @sf 1349 116 p m (i) s cmmi10.329 @sf 1372 165 p m (n) s 1155 229 p m (n) s 1224 229 p m (p) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (n) s 1420 192 p m (;) s cmti10.329 @sf 60 308 p m (and) 16 (if) ks cmmi10.329 @sf 16 r m (n) s 13 r save [ 26 26 -4 2 35] 62 @pc restore 48 r m (p) s 504 396 p m (R) s cmr10.329 @sf 13 r m (=) s cmex10.300 @sf 637 348 p m (h) s cmr10.329 @sf 677 396 p m (0) s cmmi10.329 @sf 741 396 p m (R) s cmr8.300 @sf 776 403 p m (11) s cmex10.300 @sf 834 348 p m (i) s cmmi10.329 @sf 865 396 p m (n) s 649 461 p m (m) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 11 r m (n) s 814 461 p m (n) s 913 423 p m (;) s 992 396 p m (S) s cmr10.329 @sf 15 r m (=) s cmex10.300 @sf 1112 323 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 1157 369 p m (S) s cmr8.300 @sf 1185 376 p m (11) s cmr10.329 @sf 1178 423 p m (0) s cmex10.300 @sf 1243 323 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 1277 369 p m (p) s 1277 423 p m (n) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (p) s 1178 486 p m (p) s 1424 423 p m (;) s cmti10.329 @sf 60 568 p m (wher) -1 (e) ks cmmi10.329 @sf 15 r m (n) s cmti10.329 @sf 17 r m (b) s save [<3E0000438000C0C000E06000F07000F03800003800001C00001C0007DC000C3C001C1E00180E00 180E001C0E001C07001C07001C07001C07000E03800E03800E03808703804701C04301C04381C0 2301C03300E00E00C0> 19 29 -4 9 22] 121 @pc restore cmmi10.329 @sf 38 r m (n) s cmti10.329 @sf 17 r m (matrix) s cmmi10.329 @sf 17 r m (R) s cmr8.300 @sf 516 575 p m (11) s cmti10.329 @sf 569 568 p m (and) s cmr10.329 @sf 16 r m (min) s 733 568 p m (\() s cmmi10.329 @sf m (n;) 8 (p) ks cmr10.329 @sf m (\)) s cmti10.329 @sf 15 r m (b) s save [<3E0000438000C0C000E06000F07000F03800003800001C00001C0007DC000C3C001C1E00180E00 180E001C0E001C07001C07001C07001C07000E03800E03800E03808703804701C04301C04381C0 2301C03300E00E00C0> 19 29 -4 9 22] 121 @pc restore cmr10.329 @sf 38 r m (min) s 990 568 p m (\() s cmmi10.329 @sf m (n;) 8 (p) ks cmr10.329 @sf m (\)) s cmti10.329 @sf 15 r m (matrix) s cmmi10.329 @sf 17 r m (S) s cmr8.300 @sf 1286 575 p m (11) s cmti10.329 @sf 1339 568 p m (ar) -1 (e) 15 (upp) -1 (er) 16 (triangular.) ks cmr10.329 @sf 131 692 p m (Pro) 1 (of) 16 (:) 23 (The) 17 (pro) 1 (of) 17 (is) 17 (similar) 18 (to) 16 (the) 17 (pro) 1 (of) 17 (of) 16 (the) 17 (GQR) 18 (factorization.) 24 (In) 18 (short,) 16 (one) 17 (\014rst) ks 60 749 p m (do) 1 (es) 16 (the) 15 (QR) 16 (factorization) 15 (of) ks cmmi10.329 @sf 15 r m (B) s cmr10.329 @sf 2 r m (:) s cmmi10.329 @sf 20 r m (B) s cmr10.329 @sf 16 r m (=) s cmmi10.329 @sf 12 r m (QS) s cmr10.329 @sf 3 r m (,) 15 (then) 15 (follo) 0 (ws) 14 (b) 0 (y) 15 (the) 15 (R) 0 (Q) 15 (factorization) 15 (of) ks cmmi10.329 @sf 14 r m (Q) s cmr8.300 @sf 1730 734 p m (T) s cmmi10.329 @sf 1758 749 p m (A) s cmr10.329 @sf m (.) s 20 r save [<7FFFFF80FFFFFF80C0000180C0000180C0000180C0000180C0000180C0000180C0000180C00001 80C0000180C0000180C0000180C0000180C0000180C0000180C0000180C0000180C0000180C000 0180C0000180C0000180C0000180FFFFFF807FFFFF80> 25 25 -4 -3 34] 50 @pc restore cmr10.329 @sf 131 814 p m (F) -3 (rom) 9 (the) 12 (GR) 0 (Q) 10 (factorization) 11 (form) 11 (of) ks cmmi10.329 @sf 11 r m (A) s cmr10.329 @sf 11 r m (and) s cmmi10.329 @sf 12 r m (B) s cmr10.329 @sf 2 r m (,) 12 (w) 0 (e) 10 (see) 12 (that) 11 (if) ks cmmi10.329 @sf 11 r m (B) s cmr10.329 @sf 15 r m (is) 11 (square) 12 (and) 11 (nonsingular,) ks 60 870 p m (then) 16 (the) 15 (R) 0 (Q) 15 (factorization) 15 (of) ks cmmi10.329 @sf 14 r m (B) s cmsy8.300 @sf 676 855 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 724 870 p m (A) s cmr10.329 @sf 15 r m (is) 16 (giv) 0 (en) 15 (b) 0 (y) ks 555 977 p m (\() s cmmi10.329 @sf m (B) s cmsy8.300 @sf 609 959 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 656 977 p m (A) s cmr10.329 @sf m (\)) s cmmi10.329 @sf save [<07E000000C18000038040000300200007001000070008000F0004000F0004000F0002000F00020 00F0002000780010007800100078001000780010003C0008003C0008003C0008003C0008001E00 04001E0004001E0004001E0004000F0002000F0002000F0002000F000200078001000780010007 80010007C003C07FFC1FF8> 29 32 -4 1 31] 85 @pc restore cmr10.329 @sf 49 r m (=) s cmex10.300 @sf 805 930 p m (h) s cmr10.329 @sf 845 977 p m (0) s cmmi10.329 @sf 909 977 p save [<7FFFC00001F0000000F0000000F0000000F0000000F00000007800000078000000780000007800 00003C0000003C0000003C0000003C0000001E0000001E0000001E0000001E0000000F0000000F 0000000F0000800F0010400780084007800860078008200780082003C0081003C0081803C0181E 03C0380FFFFFFC> 30 31 -1 0 27] 84 @pc restore cmex10.300 @sf 963 930 p m (i) s cmr10.329 @sf 995 977 p m (=) s cmmi10.329 @sf 13 r m (S) s cmsy8.300 @sf 1074 959 p m (\000) s cmr8.300 @sf m (1) s 1071 990 p m (11) s cmex10.300 @sf 1128 930 p m (h) s cmr10.329 @sf 1169 977 p m (0) s cmmi10.329 @sf 1233 977 p m (R) s cmr8.300 @sf 1268 984 p m (11) s cmex10.300 @sf 1325 930 p m (i) s cmmi10.329 @sf 1353 977 p m (:) s cmr10.329 @sf 131 1096 p m (With) 21 (the) 21 (decomp) 1 (osition) 23 (forms) 20 (\(1\)) 21 (and) 21 (\(2\),) 22 (w) 0 (e) 20 (presen) 0 (t) 20 (the) 21 (formal) 21 (de\014nition) 23 (for) 21 (the) ks 60 1152 p m (generalized) 17 (QR) 16 (factorizations.) ks cmbx10.329 @sf 131 1277 p save [ 34 31 -2 0 40] 68 @pc restore 40 r m (e) s save [<3FF9FFC03FF9FFC007C03E0007C03E0007C03E0007C03E0007C03E0007C03E0007C03E0007C03E 0007C03E0007C03E0007C03E0007C03E0007C03E0007C03E0007C03E0007C03E00FFFFFE00FFFF FE0007C1FE0007C0000007C0000007C0000007C0380007C07C0007C07C0003E07C0001E07C0000 F81C00007FF800000FE000> 26 32 0 0 29] 12 @pc restore 29 r m (nition:) s cmr10.329 @sf 31 r m (F) -3 (or) ks cmmi10.329 @sf 18 r m (n) s cmr10.329 @sf 21 r m (b) 0 (y) ks cmmi10.329 @sf 19 r m (m) s cmr10.329 @sf 20 r m (matrix) s cmmi10.329 @sf 20 r m (A) s cmr10.329 @sf m (,) s cmmi10.329 @sf 21 r m (n) s cmr10.329 @sf 20 r m (b) 0 (y) ks cmmi10.329 @sf 19 r m (p) s cmr10.329 @sf 20 r m (matrix) s cmmi10.329 @sf 20 r m (B) s cmr10.329 @sf 2 r m (,) 22 (w) 0 (e) 18 (call) 22 (\(1\)) 19 (as) ks cmti10.329 @sf 20 r m (the) 21 (gener) -1 (ali) ks save [<80E00041F80063FC003E0C00100200080200040100020000010000008000004000002000001000 0008000004000802000C1F0007F18003E08001C040> 18 20 -3 0 19] 122 @pc restore 18 r m (e) -2 (d) ks 60 1333 p save [<0000F0000001F8000003FC000003FE000003860000038300000101000001018001FD0080074380 800E41E0001C41700038413C0038411E0070200F00701C070070000380F00003C0F00001C0F000 01E0F00000E0F00000F0F00000F0780000787800007878000078780000783C0000783C0000381E 0000381E0000380F00003807000038078000780380007001C0007000E000E0003000E0001C01C0 000707000001FC00> 29 41 -6 9 35] 81 @pc restore 35 r m (R) 18 (factori) ks save [<80E00041F80063FC003E0C00100200080200040100020000010000008000004000002000001000 0008000004000802000C1F0007F18003E08001C040> 18 20 -3 0 19] 122 @pc restore 19 r m (ation) s cmr10.329 @sf 17 r m (\(in) 18 (short) 16 (the) 17 (GQR) 18 (factorization\)) 17 (of) ks cmmi10.329 @sf 16 r m (A) s cmr10.329 @sf 17 r m (and) s cmmi10.329 @sf 18 r m (B) s cmr10.329 @sf 2 r m (,) 18 (\(2\)) 16 (as) ks cmti10.329 @sf 17 r m (the) 18 (gener) -1 (ali) ks save [<80E00041F80063FC003E0C00100200080200040100020000010000008000004000002000001000 0008000004000802000C1F0007F18003E08001C040> 18 20 -3 0 19] 122 @pc restore 18 r m (e) -2 (d) 16 (R) ks save [<0000F0000001F8000003FC000003FE000003860000038300000101000001018001FD0080074380 800E41E0001C41700038413C0038411E0070200F00701C070070000380F00003C0F00001C0F000 01E0F00000E0F00000F0F00000F0780000787800007878000078780000783C0000783C0000381E 0000381E0000380F00003807000038078000780380007001C0007000E000E0003000E0001C01C0 000707000001FC00> 29 41 -6 9 35] 81 @pc restore 60 1390 p m (factori) s save [<80E00041F80063FC003E0C00100200080200040100020000010000008000004000002000001000 0008000004000802000C1F0007F18003E08001C040> 18 20 -3 0 19] 122 @pc restore 19 r m (ation) s cmr10.329 @sf 15 r m (\(in) 16 (short) 15 (the) 15 (GR) 0 (Q) 14 (factorization\)) 15 (of) ks cmmi10.329 @sf 15 r m (A) s cmr10.329 @sf 15 r m (and) s cmmi10.329 @sf 15 r m (B) s cmr10.329 @sf 2 r m (.) s 131 1515 p m (Discussion:) 19 (the) 13 (other) 12 (p) 1 (ossible) 15 (generalized) 14 (QR) 14 (factorization) 12 (forms.) 19 (F) -3 (or) 11 (example,) 13 (the) 13 (QR) ks 60 1571 p m (factorizaiton) 15 (of) ks cmmi10.329 @sf 15 r m (B) s cmr8.300 @sf 412 1556 p m (T) s cmmi10.329 @sf 440 1571 p m (A) s cmr10.329 @sf m (.) s 20 r save [ 44 1 0 -12 45] 124 @pc restore 61 r m (will) 16 (write) 16 (later.) ks cmbx10.432 @sf 60 1723 p save [<00FF800007FFF0001FFFFC003F01FE007C007F007E007F80FF007FC0FF003FC0FF003FE0FF003F E07E003FE03C003FE000003FE000003FE000003FC000003FC000007F8000007F0000007E000001 FC0000FFF00000FFC0000007F0000001F8000001FC000000FE000000FF000000FF000F007F801F 807F803F807F803F807F803F807F803F80FF001F00FF000F81FE0007FFFC0003FFF000007F8000> 27 39 -3 0 34] 51 @pc restore 163 1723 p save [<00007FF003000003FFFE0F00001FFFFF1F00003FF007BF0000FF8001FF0001FE0000FF0003F800 00FF0007F00000FF000FF00000FF001FE00000FF001FE00000FF003FC00000FF003FC00000FF00 7FC00000FF007F8001FFFFF87F8001FFFFF8FF8001FFFFF8FF8000000000FF8000000000FF8000 000000FF8000000000FF8000000000FF8000000000FF8000000000FF80000000007F8000000000 7F80000007007FC0000007003FC0000007003FC000000F001FE000000F001FE000000F000FF000 001F0007F000003F0003F800003F0001FE0000FF0000FF8001FF00003FF00FFF00001FFFFF0F00 0003FFFC070000007FE00300> 45 41 -4 0 54] 71 @pc restore 54 r m (eneral) s save [ 15 43 -3 0 20] 105 @pc restore 20 r save [ 25 27 -2 0 31] 122 @pc restore 31 r m (e) -1 (d) ks 21 r save [<00000000780000000001FE0000000003FF0000000003FF8000000007FF8000000007FFC0000000 0FFFC00000000FFFC00000000FFFE00000000F81E00000001F00600000001E00600000FFFE0060 000FFFFE0000003FE07F800000FFC03FE00001FCC037F00003F8C063F80007F060C1FC000FF03F 81FE001FE01F00FF001FE00000FF003FC000007F803FC000007F807FC000007FC07F8000003FC0 7F8000003FC0FF8000003FE0FF8000003FE0FF8000003FE0FF8000003FE0FF8000003FE0FF8000 003FE0FF8000003FE0FF8000003FE0FF8000003FE0FF8000003FE07F8000003FC07F8000003FC0 7FC000007FC07FC000007FC03FC000007F803FC000007F801FE00000FF001FE00000FF000FF000 01FE0007F00001FC0003F80003F80001FC0007F000007F001FC000003FC07F80000007FFFC0000 0000FFE00000> 43 53 -4 12 52] 81 @pc restore 52 r m (R) s 23 r save [ 36 41 -3 0 43] 70 @pc restore 38 r m (actor) s save [ 15 43 -3 0 20] 105 @pc restore 20 r save [ 25 27 -2 0 31] 122 @pc restore 31 r m (at) s save [ 15 43 -3 0 20] 105 @pc restore 19 r m (on) s 22 r save [<00078003C00000078003C000000FC007E000000FC007E000000FC007E000001FE00FF000001FE0 0FF000003FF01FF800003FF01FB800003FF01FB800007F783F3C00007F383F1C0000FF383F1E00 00FE1C7E0E0000FE1C7E0E0001FE1EFC0F0001FC0EFC070001FC0EFC070003F807F8038003F807 F8038007F807F803C007F003F001C007F003F001C00FE007E000E0FFFE7FFC0FFEFFFE7FFC0FFE FFFE7FFC0FFE> 47 27 -1 0 50] 119 @pc restore 50 r save [ 15 43 -3 0 20] 105 @pc restore 20 r m (t) s save [ 33 42 -3 0 38] 104 @pc restore 59 r save [ 39 41 -3 0 47] 80 @pc restore 47 r save [ 15 43 -3 0 20] 105 @pc restore 20 r save [<0001C000000003E000000003E000000007F000000007F00000000FF80000000FF80000000FF800 00001FDC0000001FDC0000003FDE0000003F8E0000007F8F0000007F070000007F07000000FE03 800000FE03800001FC01C00001FC01C00003FC01E00003F800E00007F800F00007F000700007F0 007000FFFE03FF80FFFE03FF80FFFE03FF80> 33 27 -1 0 36] 118 @pc restore 35 r m (ot) s save [ 15 43 -3 0 20] 105 @pc restore 20 r m (n) s save [<007FF00003FFFE000FC01F801F0007C03C0001E07C0001F0F80000F8F80000F8F80000F8F80000 F87C0001F83E0007F01FFFFFF007FFFFE00FFFFFC01FFFFF801FFFFF003FFFF8003E0000003C00 0000380000003800000018FF80001FFFE0000FC1F8001F80FC001F007C003F007E007F007F007F 007F007F007F007F007F007F007F007F007F003F007E101F007C381F80FC7C0FC1FE7C03FFE7F8 00FF81F0> 30 40 -2 13 34] 103 @pc restore cmr10.329 @sf 60 1832 p m (The) 10 (previous) 11 (section) 11 (in) 0 (tro) 1 (duces) 10 (the) 11 (generalized) 12 (QR) 11 (factorization.) 18 (As) 10 (in) 11 (the) 10 (QR) 11 (factorization) ks 60 1889 p m (of) 16 (a) 15 (matrix,) 16 (w) 0 (e) 15 (can) 16 (also) 16 (incorp) 1 (orate) 17 (the) 16 (piv) 0 (oting) 15 (tec) 0 (hnique) 17 (in) 0 (to) 15 (the) 16 (GQR) 17 (factorization) 16 (to) ks 60 1945 p m (deal) 16 (with) 15 (the) 16 (rank) 15 (de\014cien) 0 (t) 15 (case) 15 (of) 15 (the) 16 (factorization.) ks cmbx10.329 @sf 131 2070 p save [<0007FC0600003FFF8E0000FE01FE0003F000FE0007E0007E000FC0007E001F80007E003F00007E 003F00007E007F00007E007E00007E007E00007E00FE003FFFE0FE003FFFE0FE00000000FE0000 0000FE00000000FE00000000FE000000007E000006007E000006007F000006003F00000E003F00 000E001F80001E000FC0001E0007E0003E0003F000FE0000FE03DE00003FFF0E000007FC0200> 35 31 -3 0 41] 71 @pc restore 41 r save [<000000F0000001F8000003FC000007FE000007FE000007FF00000FFF00000F0700000E03001FFE 0300FFFF0001F81F8007F81FE00FD833F01F8FE1F83F87C1FC3F0000FC7F0000FE7E00007E7E00 007EFE00007FFE00007FFE00007FFE00007FFE00007FFE00007FFE00007FFE00007FFE00007F7E 00007E7F0000FE7F0000FE3F0000FC1F8001F81F8001F80FC003F007E007E001F81F8000FFFF00 001FF800> 32 40 -3 9 39] 81 @pc restore 39 r save [ 36 31 -2 0 39] 82 @pc restore 56 r m (factori) s save [ 19 20 -1 0 23] 122 @pc restore 23 r m (at) 1 (ion) ks 20 r save [<0030018000007803C000007803C000007803C00000FC07E00000FC07E00001F60FB00001F60F30 0001F60F300003E31E180003E31E180007C1BE0C0007C1BC0C0007C1BC0C000F80F806000F80F8 06001F00F803001F00F00300FFE7FE1FE0FFE7FE1FE0> 35 20 -1 0 38] 119 @pc restore 38 r m (it) s save [ 24 32 -3 0 29] 104 @pc restore 47 r m (column) s 15 r save [ 24 29 -2 9 29] 112 @pc restore 29 r m (iv) 0 (otin) ks save [<01FF000FFFE03F01F878003C78003CF0001EF0001EF0001E70003E3C007C1FFFFC07FFF80FFFF0 1FFF801C000018000018000009FC000FFF000F07801E03C03E03E03E03E03E03E03E03E03E03E0 1E03DE0F079E07FFFE01FC3C> 23 30 -1 10 26] 103 @pc restore cmr10.329 @sf 26 r m (:) s cmti10.329 @sf 20 r save [ 25 31 -3 0 29] 76 @pc restore 28 r m (et) s cmmi10.329 @sf 14 r m (A) s cmti10.329 @sf 17 r m (b) -1 (e) 14 (an) ks cmmi10.329 @sf 16 r m (n) s cmti10.329 @sf 17 r m (b) s save [<3E0000438000C0C000E06000F07000F03800003800001C00001C0007DC000C3C001C1E00180E00 180E001C0E001C07001C07001C07001C07000E03800E03800E03808703804701C04301C04381C0 2301C03300E00E00C0> 19 29 -4 9 22] 121 @pc restore cmmi10.329 @sf 38 r m (m) s cmti10.329 @sf 16 r m (matrix,) s cmmi10.329 @sf 17 r m (B) s cmti10.329 @sf 19 r m (b) -1 (e) 15 (an) ks cmmi10.329 @sf 16 r m (n) s cmti10.329 @sf 60 2126 p m (b) s save [<3E0000438000C0C000E06000F07000F03800003800001C00001C0007DC000C3C001C1E00180E00 180E001C0E001C07001C07001C07001C07000E03800E03800E03808703804701C04301C04381C0 2301C03300E00E00C0> 19 29 -4 9 22] 121 @pc restore cmmi10.329 @sf 36 r m (p) s cmti10.329 @sf 14 r m (matrix,) 16 (then) 14 (ther) -1 (e) 13 (ar) -1 (e) 13 (ortho) -1 (gonal) 14 (matric) -1 (es) ks cmmi10.329 @sf 13 r m (Q) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (n) s cmsy10.329 @sf 6 r m (\002) s cmmi10.329 @sf 6 r m (n) s cmr10.329 @sf m (\)) s cmti10.329 @sf m (,) s cmmi10.329 @sf 14 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr10.329 @sf 37 r m (\() s cmmi10.329 @sf m (p) s cmsy10.329 @sf 6 r m (\002) s cmmi10.329 @sf 6 r m (p) s cmr10.329 @sf m (\)) s cmti10.329 @sf m (,) 14 (and) ks cmmi10.329 @sf 14 r m (n) s cmti10.329 @sf 14 r m (b) s save [<3E0000438000C0C000E06000F07000F03800003800001C00001C0007DC000C3C001C1E00180E00 180E001C0E001C07001C07001C07001C07000E03800E03800E03808703804701C04301C04381C0 2301C03300E00E00C0> 19 29 -4 9 22] 121 @pc restore cmmi10.329 @sf 37 r m (n) s cmti10.329 @sf 14 r m (p) -1 (ermutation) ks 60 2183 p m (matrix) s cmmi10.329 @sf 17 r m (P) s cmti10.329 @sf 23 r m (such) 16 (that) ks cmmi10.329 @sf 703 2239 p m (Q) s cmr8.300 @sf 739 2221 p m (T) s cmmi10.329 @sf 766 2239 p m (AP) s cmr10.329 @sf 19 r m (=) s cmmi10.329 @sf 13 r m (R) 0 (;) 45 (Q) ks cmr8.300 @sf 1025 2221 p m (T) s cmmi10.329 @sf 1053 2239 p m (B) s 2 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr10.329 @sf 50 r m (=) s cmmi10.329 @sf 13 r m (S) s cmr10.329 @sf 1802 2239 p m (\(3\)) s cmti10.329 @sf 60 2323 p m (assumes) 16 (one) 16 (of) 16 (the) 17 (fol) 2 (lowing) 15 (forms) ks save [ 8 20 -5 0 14] 58 @pc restore 60 2379 p m (if) s cmmi10.329 @sf 16 r m (n) s cmsy10.329 @sf 13 r save [ 26 36 -4 7 35] 20 @pc restore cmmi10.329 @sf 48 r m (p) s 240 2538 p m (R) s cmr10.329 @sf 13 r m (=) s cmex10.300 @sf 365 2439 p save [ 14 74 -13 73 28] 50 @pc restore 365 2513 p m (6) s 365 2540 p save [ 14 74 -13 72 28] 52 @pc restore cmmi10.329 @sf 413 2480 p m (R) s cmr8.300 @sf 448 2487 p m (11) s cmmi10.329 @sf 527 2480 p m (R) s cmr8.300 @sf 562 2487 p m (12) s cmr10.329 @sf 438 2536 p m (0) s 551 2536 p m (0) s 438 2593 p m (0) s 551 2593 p m (0) s cmex10.300 @sf 619 2439 p save [<001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C00 1C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C 001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C00 1C001C001C001C001C001C001C001C001C001C001C001C001CFFFCFFFCFFFC> 14 74 0 73 28] 51 @pc restore 619 2513 p m (7) s 619 2540 p save [ 14 74 0 72 28] 53 @pc restore cmmi10.329 @sf 656 2480 p m (q) s 656 2536 p save [<600F00E01880701880703840703840703840381C203838003838003870001FC0001E00001D0000 1C80000E40600E20F00E10F00E08700706100701E0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 20 32 -2 0 24] 107 @pc restore 656 2593 p m (n) s cmsy10.329 @sf 11 r m (\000) s cmmi10.329 @sf 10 r m (q) s cmsy10.329 @sf 12 r m (\000) s cmmi10.329 @sf 10 r save [<600F00E01880701880703840703840703840381C203838003838003870001FC0001E00001D0000 1C80000E40600E20F00E10F00E08700706100701E0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 20 32 -2 0 24] 107 @pc restore 415 2652 p m (q) s 479 2652 p m (m) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (q) s 883 2565 p m (;) s 975 2538 p m (S) s cmr10.329 @sf 15 r m (=) s cmex10.300 @sf 1106 2439 p save [ 14 74 -13 73 28] 50 @pc restore 1106 2513 p m (6) s 1106 2540 p save [ 14 74 -13 72 28] 52 @pc restore cmr10.329 @sf 1155 2480 p m (0) s cmmi10.329 @sf 1219 2480 p m (S) s cmr8.300 @sf 1247 2487 p m (11) s cmmi10.329 @sf 1326 2480 p m (S) s cmr8.300 @sf 1354 2487 p m (12) s cmr10.329 @sf 1155 2536 p m (0) s 1240 2536 p m (0) s cmmi10.329 @sf 1326 2536 p m (S) s cmr8.300 @sf 1354 2543 p m (22) s cmr10.329 @sf 1155 2593 p m (0) s 1240 2593 p m (0) s 1347 2593 p m (0) s cmex10.300 @sf 1412 2439 p save [<001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C00 1C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C 001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C00 1C001C001C001C001C001C001C001C001C001C001C001C001CFFFCFFFCFFFC> 14 74 0 73 28] 51 @pc restore 1412 2513 p m (7) s 1412 2540 p save [ 14 74 0 72 28] 53 @pc restore cmmi10.329 @sf 1461 2480 p m (q) s 1461 2536 p save [<600F00E01880701880703840703840703840381C203838003838003870001FC0001E00001D0000 1C80000E40600E20F00E10F00E08700706100701E0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 20 32 -2 0 24] 107 @pc restore 1461 2593 p m (n) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 11 r m (q) s cmsy10.329 @sf 12 r m (\000) s cmmi10.329 @sf 10 r save [<600F00E01880701880703840703840703840381C203838003838003870001FC0001E00001D0000 1C80000E40600E20F00E10F00E08700706100701E0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 20 32 -2 0 24] 107 @pc restore 1115 2652 p m (p) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 11 r m (n) s 1263 2652 p m (q) s 1326 2652 p m (n) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 11 r m (q) s 1688 2565 p m (;) s @eop 4 @bop0 4 @bop1 cmsl10.329 @sf 60 -99 p m (The) 15 (Generalized) 17 (QR) 16 (Decomp) 1 (osition) ks cmr10.329 @sf 1059 r m (4) s cmti10.329 @sf 60 45 p m (wher) -1 (e) ks cmmi10.329 @sf 15 r m (m) s cmti10.329 @sf 17 r m (b) s save [<3E0000438000C0C000E06000F07000F03800003800001C00001C0007DC000C3C001C1E00180E00 180E001C0E001C07001C07001C07001C07000E03800E03800E03808703804701C04301C04381C0 2301C03300E00E00C0> 19 29 -4 9 22] 121 @pc restore cmmi10.329 @sf 38 r m (m) s cmti10.329 @sf 16 r m (matrix) s cmmi10.329 @sf 17 r m (R) s cmr8.300 @sf 541 52 p m (11) s cmti10.329 @sf 594 45 p m (and) s cmmi10.329 @sf 16 r m (p) s cmti10.329 @sf 16 r m (b) s save [<3E0000438000C0C000E06000F07000F03800003800001C00001C0007DC000C3C001C1E00180E00 180E001C0E001C07001C07001C07001C07000E03800E03800E03808703804701C04301C04381C0 2301C03300E00E00C0> 19 29 -4 9 22] 121 @pc restore cmmi10.329 @sf 39 r m (p) s cmti10.329 @sf 16 r m (matrix) s cmmi10.329 @sf 17 r m (S) s cmr8.300 @sf 994 52 p m (21) s cmti10.329 @sf 1047 45 p m (ar) -1 (e) 16 (upp) -1 (er) 15 (triangular.) ks 131 170 p save [ 30 31 -3 0 31] 80 @pc restore 31 r m (r) -1 (o) -2 (of) ks save [ 8 20 -5 0 14] 58 @pc restore cmr10.329 @sf 32 r m (The) 16 (pro) 1 (of) 15 (is) 15 (constructiv) 0 (e.) 20 (By) 15 (the) 15 (QR) 16 (factorization) 15 (of) ks cmmi10.329 @sf 15 r m (A) s cmr10.329 @sf 15 r m (w) 0 (e) 14 (ha) 0 (v) -1 (e) ks cmmi10.329 @sf 703 292 p m (Q) s cmr8.300 @sf 739 276 p m (T) s cmmi10.329 @sf 766 292 p m (A) s cmr10.329 @sf 13 r m (=) s cmex10.300 @sf 890 218 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 935 264 p m (R) s cmr8.300 @sf 970 271 p m (11) s cmr10.329 @sf 959 318 p m (0) s cmex10.300 @sf 1028 218 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 1061 264 p m (m) s 1061 318 p m (n) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 11 r m (m) s 951 381 p m (m) s 1225 319 p m (:) s cmr10.329 @sf 60 475 p m (Let) s cmmi10.329 @sf 15 r m (Q) s cmr8.300 @sf 177 460 p m (T) s cmr10.329 @sf 219 475 p m (prem) 0 (ultiply) 15 (on) ks cmmi10.329 @sf 15 r m (B) s cmr10.329 @sf 2 r m (,) 15 (then) 15 (the) 15 (desired) 16 (factorizations) 14 (follo) 0 (w) 14 (up) 1 (on) 15 (the) 15 (R) 0 (Q) 14 (factorization) ks 60 531 p m (of) s cmmi10.329 @sf 15 r m (Q) s cmr8.300 @sf 148 516 p m (T) s cmmi10.329 @sf 175 531 p m (B) s cmr10.329 @sf 2 r m (;) 16 (if) ks cmmi10.329 @sf 15 r m (n) s cmsy10.329 @sf 13 r save [ 26 36 -4 7 35] 20 @pc restore cmmi10.329 @sf 48 r m (p) s cmr10.329 @sf m (,) s 699 594 p m (\() s cmmi10.329 @sf m (Q) s cmr8.300 @sf 753 579 p m (T) s cmmi10.329 @sf 781 594 p m (B) s cmr10.329 @sf 2 r m (\)) s cmmi10.329 @sf save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr10.329 @sf 49 r m (=) s cmex10.300 @sf 964 546 p m (h) s cmr10.329 @sf 1004 594 p m (0) s cmmi10.329 @sf 1069 594 p m (S) s cmr8.300 @sf 1097 601 p m (11) s cmex10.300 @sf 1155 546 p m (i) s cmmi10.329 @sf 1181 594 p m (n) s 982 659 p m (p) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (n) s 1129 659 p m (n) s 1229 621 p m (:) s cmr10.329 @sf 60 739 p m (otherwise,) 15 (the) 15 (R) 0 (Q) 15 (factorization) 15 (of) ks cmmi10.329 @sf 15 r m (B) s cmsy8.300 @sf 788 724 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 836 739 p m (A) s cmr10.329 @sf 15 r m (is) 16 (of) 14 (the) 16 (form) ks 677 860 p m (\() s cmmi10.329 @sf m (Q) s cmr8.300 @sf 731 845 p m (T) s cmmi10.329 @sf 759 860 p m (B) s cmr10.329 @sf 2 r m (\)) s cmmi10.329 @sf save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr10.329 @sf 49 r m (=) s cmex10.300 @sf 939 787 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 984 833 p m (S) s cmr8.300 @sf 1012 840 p m (11) s cmmi10.329 @sf 984 887 p m (S) s cmr8.300 @sf 1012 894 p m (21) s cmex10.300 @sf 1070 787 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 1103 833 p m (n) s cmsy10.329 @sf 11 r m (\000) s cmmi10.329 @sf 10 r m (p) s 1103 887 p m (p) s 1005 950 p m (p) s 1251 887 p m (:) s 60 1025 p save [<7FFFFF80FFFFFF80C0000180C0000180C0000180C0000180C0000180C0000180C0000180C00001 80C0000180C0000180C0000180C0000180C0000180C0000180C0000180C0000180C0000180C000 0180C0000180C0000180C0000180FFFFFF807FFFFF80> 25 25 -4 -3 34] 50 @pc restore cmr10.329 @sf 34 r m (.) s 131 1089 p m (Occasionally) -3 (,) 20 (one) 20 (wishes) 19 (to) 19 (compute) 19 (the) 19 (QR) 20 (factorizations) 19 (of) ks cmmi10.329 @sf 18 r m (B) s cmsy8.300 @sf 1436 1074 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 1484 1089 p m (A) s cmr10.329 @sf m (,) 20 (for) 18 (example,) 21 (to) ks 60 1146 p m (solv) 0 (e) 14 (w) 0 (eigh) 0 (ted) 14 (least) 15 (square) 15 (problem) ks 762 1236 p m (min) s cmmi8.300 @sf 790 1261 p m (x) s cmsy10.329 @sf 845 1236 p m (k) s cmmi10.329 @sf m (B) s cmsy8.300 @sf 904 1218 p m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 952 1236 p m (\() s cmmi10.329 @sf m (Ax) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (b) s cmr10.329 @sf m (\)) s cmsy10.329 @sf m (k) s cmmi10.329 @sf m (:) s cmr10.329 @sf 60 1341 p m (T) -3 (o) 19 (a) 0 (v) -1 (oid) 19 (forming) ks cmmi10.329 @sf 20 r m (B) s cmsy8.300 @sf 466 1326 p m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 535 1341 p m (and) s cmmi10.329 @sf 20 r m (B) s cmsy8.300 @sf 664 1326 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 712 1341 p m (A) s cmr10.329 @sf m (,) 21 (w) 0 (e) 20 (note) 20 (that) 19 (the) 21 (GQR) 21 (factorization) 20 (\(1\)) 19 (of) ks cmmi10.329 @sf 20 r m (A) s cmr10.329 @sf 21 r m (and) s cmmi10.329 @sf 20 r m (B) s cmr10.329 @sf 60 1398 p m (implici) 1 (tly) 17 (giv) 0 (es) 15 (the) 15 (QR) 16 (factorization) ks cmmi10.329 @sf 15 r m (B) s cmsy8.300 @sf 837 1383 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 885 1398 p m (A) s cmr10.329 @sf m (:) s cmmi10.329 @sf 596 1518 p save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr8.300 @sf 632 1500 p m (T) s cmr10.329 @sf 660 1518 p m (\() s cmmi10.329 @sf m (B) s cmsy8.300 @sf 714 1500 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 761 1518 p m (A) s cmr10.329 @sf m (\)) 13 (=) ks cmex10.300 @sf 874 1446 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 919 1491 p save [<7FFFC00001F0000000F0000000F0000000F0000000F00000007800000078000000780000007800 00003C0000003C0000003C0000003C0000001E0000001E0000001E0000001E0000000F0000000F 0000000F0000800F0010400780084007800860078008200780082003C0081003C0081803C0181E 03C0380FFFFFFC> 30 31 -1 0 27] 84 @pc restore cmr10.329 @sf 924 1546 p m (0) s cmex10.300 @sf 972 1446 p save [ 12 124 0 122 24] 35 @pc restore cmr10.329 @sf 1009 1518 p m (=) s cmmi10.329 @sf 13 r m (S) s cmsy8.300 @sf 1088 1500 p m (\000) s cmr8.300 @sf m (1) s 1085 1530 p m (11) s cmex10.300 @sf 1142 1446 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 1187 1491 p m (R) s cmr8.300 @sf 1222 1498 p m (11) s cmr10.329 @sf 1212 1546 p m (0) s cmex10.300 @sf 1280 1446 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 1312 1518 p m (;) s cmr10.329 @sf 60 1645 p m (i.e,) 15 (the) 16 (upp) 1 (er) 16 (triangular) 15 (part) ks cmmi10.329 @sf 15 r save [<7FFFC00001F0000000F0000000F0000000F0000000F00000007800000078000000780000007800 00003C0000003C0000003C0000003C0000001E0000001E0000001E0000001E0000000F0000000F 0000000F0000800F0010400780084007800860078008200780082003C0081003C0081803C0181E 03C0380FFFFFFC> 30 31 -1 0 27] 84 @pc restore cmr10.329 @sf 48 r m (of) 14 (the) 16 (QR) 16 (factorization) 15 (of) ks cmmi10.329 @sf 14 r m (B) s cmsy8.300 @sf 1266 1630 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 1314 1645 p m (A) s cmr10.329 @sf 16 r m (can) 15 (b) 1 (e) 16 (determined) 16 (b) 0 (y) ks cmmi10.329 @sf 838 1735 p m (S) s cmr8.300 @sf 866 1742 p m (11) s cmmi10.329 @sf 904 1735 p save [<7FFFC00001F0000000F0000000F0000000F0000000F00000007800000078000000780000007800 00003C0000003C0000003C0000003C0000001E0000001E0000001E0000001E0000000F0000000F 0000000F0000800F0010400780084007800860078008200780082003C0081003C0081803C0181E 03C0380FFFFFFC> 30 31 -1 0 27] 84 @pc restore cmr10.329 @sf 45 r m (=) s cmmi10.329 @sf 13 r m (R) s cmr8.300 @sf 1032 1742 p m (11) s cmmi10.329 @sf 1069 1735 p m (:) s cmr10.329 @sf 60 1825 p m (Hence,) 13 (the) 11 (p) 1 (ossible) 13 (n) 0 (umerical) 11 (di) ks save [<7FE3FE3FF007007007000700700700070070070007007007000700700700070070070007007007 000700700700070070070007007007000700700700070070070007007007000700700700070070 0700070070070007007007000700700700FFFFFFFF000700700000070070000007007000000700 700000070070000007007000000700F00F000300F00F000380F80F0001C07C060000F04F040000 1F81F800> 36 32 0 0 38] 14 @pc restore 38 r m (cultie) 1 (s) 13 (to) 10 (use,) 12 (explici) 1 (tly) 13 (or) 11 (implici) 1 (tly) -3 (,) 13 (the) 11 (QR) 12 (factorization) ks 60 1882 p m (of) s cmmi10.329 @sf 15 r m (B) s cmsy8.300 @sf 148 1867 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 196 1882 p m (A) s cmr10.329 @sf 15 r m (is) 16 (con\014ned) 16 (to) 14 (the) 16 (condition) 16 (n) 0 (um) 0 (b) 1 (er) 14 (of) ks cmmi10.329 @sf 15 r m (S) s cmr8.300 @sf 1049 1889 p m (11) s cmr10.329 @sf 1086 1882 p m (.) s 131 1947 p m (Moreo) -1 (v) -1 (er,) 13 (if) 16 (w) 0 (e) 14 (partition) ks cmmi10.329 @sf 15 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr10.329 @sf 49 r m (=) s cmex10.300 @sf 738 1900 p m (h) s cmmi10.329 @sf 779 1947 p save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr8.300 @sf 806 1954 p m (1) s cmmi10.329 @sf 866 1947 p save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr8.300 @sf 893 1954 p m (2) s cmex10.300 @sf 933 1900 p m (i) s cmr10.329 @sf 968 1947 p m (where) s cmmi10.329 @sf 16 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr8.300 @sf 1127 1954 p m (1) s cmr10.329 @sf 1161 1947 p m (has) s cmmi10.329 @sf 15 r m (m) s cmr10.329 @sf 15 r m (columns,) 16 (then) ks cmmi10.329 @sf 749 2051 p m (B) s cmsy8.300 @sf 785 2033 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 833 2051 p m (A) s cmr10.329 @sf 12 r m (=) s cmmi10.329 @sf 13 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr8.300 @sf 954 2058 p m (1) s cmr10.329 @sf 974 2051 p m (\() s cmmi10.329 @sf m (S) s cmsy8.300 @sf 1023 2033 p m (\000) s cmr8.300 @sf m (1) s 1020 2064 p m (11) s cmmi10.329 @sf 1069 2051 p m (R) s cmr8.300 @sf 1104 2058 p m (11) s cmr10.329 @sf 1141 2051 p m (\)) s cmmi10.329 @sf m (:) s cmr10.329 @sf 60 2141 p m (This) 19 (sho) 0 (ws) 17 (that) 18 (if) ks cmmi10.329 @sf 19 r m (A) s cmr10.329 @sf 19 r m (is) 19 (of) 18 (rank) ks cmmi10.329 @sf 19 r m (m) s cmr10.329 @sf m (,) 18 (the) 19 (columns) 20 (of) ks cmmi10.329 @sf 18 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr8.300 @sf 1130 2148 p m (1) s cmr10.329 @sf 1168 2141 p m (form) 17 (an) 19 (orthonormal) 18 (basis) 19 (for) 18 (the) ks 60 2198 p m (space) 15 (spanned) 16 (b) 0 (y) 14 (the) 15 (columns) 16 (of) ks cmmi10.329 @sf 15 r m (B) s cmsy8.300 @sf 764 2183 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 812 2198 p m (A) s cmr10.329 @sf m (.) 20 (The) 15 (matrix) ks cmmi10.329 @sf 15 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr8.300 @sf 1147 2205 p m (1) s cmmi10.329 @sf 1166 2198 p save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr8.300 @sf 1203 2183 p m (T) s 1193 2209 p m (1) s cmr10.329 @sf 1245 2198 p m (is) 16 (the) 15 (orthogonal) 14 (pro) 3 (jection) 15 (on) ks 60 2254 p m (the) 15 (column) 16 (space) 16 (of) ks cmmi10.329 @sf 15 r m (B) s cmsy8.300 @sf 507 2239 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 555 2254 p m (A) s cmr10.329 @sf m (.) s 131 2319 p m (When) s cmmi10.329 @sf 11 r m (A) s cmr10.329 @sf 11 r m (is) s cmmi10.329 @sf 12 r m (n) s cmr10.329 @sf 11 r m (b) 0 (y) ks cmmi10.329 @sf 10 r m (m) s cmr10.329 @sf 11 r m (matrix) 10 (with) ks cmmi10.329 @sf 12 r m (n) s 13 r save [<000001C00000078000001E00000078000001E00000078000000E00000038000000F0000003C000 000F0000003C000000F0000000F00000003C0000000F00000003C0000000F0000000380000000E 0000000780000001E0000000780000001E0000000780000001C0> 26 26 -4 2 35] 60 @pc restore 48 r m (m) s cmr10.329 @sf m (,) 11 (although) 11 (it) 11 (still) 13 (can) 11 (b) 1 (e) 12 (presen) 0 (ted) 10 (the) 11 (similar) 12 (GQR) ks 60 2376 p m (factorization) 12 (form) 11 (of) ks cmmi10.329 @sf 12 r m (A) s cmr10.329 @sf 12 r m (and) s cmmi10.329 @sf 13 r m (B) s cmr10.329 @sf 2 r m (,) 13 (it) 12 (is) 13 (more) 11 (useful) 14 (in) 13 (applications) 13 (to) 12 (represen) 0 (t) 11 (the) 12 (factorization) ks 60 2432 p m (as) 15 (the) 15 (follo) 0 (wing:) ks cmbx10.329 @sf 131 2557 p save [<0007FC0600003FFF8E0000FE01FE0003F000FE0007E0007E000FC0007E001F80007E003F00007E 003F00007E007F00007E007E00007E007E00007E00FE003FFFE0FE003FFFE0FE00000000FE0000 0000FE00000000FE00000000FE000000007E000006007E000006007F000006003F00000E003F00 000E001F80001E000FC0001E0007E0003E0003F000FE0000FE03DE00003FFF0E000007FC0200> 35 31 -3 0 41] 71 @pc restore 41 r save [ 36 31 -2 0 39] 82 @pc restore 39 r save [<000000F0000001F8000003FC000007FE000007FE000007FF00000FFF00000F0700000E03001FFE 0300FFFF0001F81F8007F81FE00FD833F01F8FE1F83F87C1FC3F0000FC7F0000FE7E00007E7E00 007EFE00007FFE00007FFE00007FFE00007FFE00007FFE00007FFE00007FFE00007FFE00007F7E 00007E7F0000FE7F0000FE3F0000FC1F8001F81F8001F80FC003F007E007E001F81F8000FFFF00 001FF800> 32 40 -3 9 39] 81 @pc restore 54 r m (factori) s save [ 19 20 -1 0 23] 122 @pc restore 23 r m (ati) 1 (on:) ks cmti10.329 @sf 21 r save [ 25 31 -3 0 29] 76 @pc restore 28 r m (et) s cmmi10.329 @sf 14 r m (A) s cmti10.329 @sf 15 r m (b) -1 (e) 14 (an) ks cmmi10.329 @sf 16 r m (n) s cmti10.329 @sf 15 r m (b) s save [<3E0000438000C0C000E06000F07000F03800003800001C00001C0007DC000C3C001C1E00180E00 180E001C0E001C07001C07001C07001C07000E03800E03800E03808703804701C04301C04381C0 2301C03300E00E00C0> 19 29 -4 9 22] 121 @pc restore cmmi10.329 @sf 38 r m (m) s cmti10.329 @sf 15 r m (matrix,) s cmmi10.329 @sf 17 r m (B) s cmti10.329 @sf 18 r m (b) -1 (e) 14 (an) ks cmmi10.329 @sf 15 r m (n) s cmti10.329 @sf 16 r m (b) s save [<3E0000438000C0C000E06000F07000F03800003800001C00001C0007DC000C3C001C1E00180E00 180E001C0E001C07001C07001C07001C07000E03800E03800E03808703804701C04301C04381C0 2301C03300E00E00C0> 19 29 -4 9 22] 121 @pc restore cmmi10.329 @sf 37 r m (p) s cmti10.329 @sf 16 r m (matrix,) s cmmi10.329 @sf 16 r m (n) s 13 r save [<000001C00000078000001E00000078000001E00000078000000E00000038000000F0000003C000 000F0000003C000000F0000000F00000003C0000000F00000003C0000000F0000000380000000E 0000000780000001E0000000780000001E0000000780000001C0> 26 26 -4 2 35] 60 @pc restore 48 r m (m) s cmti10.329 @sf m (,) 15 (then) ks 60 2613 p m (ther) -1 (e) 15 (ar) -1 (e) 15 (ortho) -1 (gonal) 16 (matric) -1 (es) ks cmmi10.329 @sf 15 r m (Q) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (n) s cmsy10.329 @sf 10 r m (\002) s cmmi10.329 @sf 10 r m (n) s cmr10.329 @sf m (\)) s cmti10.329 @sf 17 r m (and) s cmmi10.329 @sf 16 r save [<07E000000C18000038040000300200007001000070008000F0004000F0004000F0002000F00020 00F0002000780010007800100078001000780010003C0008003C0008003C0008003C0008001E00 04001E0004001E0004001E0004000F0002000F0002000F0002000F000200078001000780010007 80010007C003C07FFC1FF8> 29 32 -4 1 31] 85 @pc restore cmr10.329 @sf 36 r m (\() s cmmi10.329 @sf m (m) s cmsy10.329 @sf 10 r m (\002) s cmmi10.329 @sf 10 r m (m) s cmr10.329 @sf m (\)) s cmti10.329 @sf 16 r m (such) 16 (that) ks cmmi10.329 @sf 702 2704 p m (Q) s cmr8.300 @sf 738 2686 p m (T) s cmmi10.329 @sf 765 2704 p m (A) s save [<07E000000C18000038040000300200007001000070008000F0004000F0004000F0002000F00020 00F0002000780010007800100078001000780010003C0008003C0008003C0008003C0008001E00 04001E0004001E0004001E0004000F0002000F0002000F0002000F000200078001000780010007 80010007C003C07FFC1FF8> 29 32 -4 1 31] 85 @pc restore cmr10.329 @sf 49 r m (=) s cmmi10.329 @sf 13 r m (R) 0 (;) 83 (Q) ks cmr8.300 @sf 1063 2686 p m (T) s cmmi10.329 @sf 1090 2704 p m (B) s cmr10.329 @sf 16 r m (=) s cmmi10.329 @sf 13 r m (S) s cmr10.329 @sf 1802 2704 p m (\(2\)) s @eop 3 @bop0 3 @bop1 cmsl10.329 @sf 60 -99 p m (The) 15 (Generalized) 17 (QR) 16 (Decomp) 1 (osition) ks cmr10.329 @sf 1059 r m (3) s 60 45 p m (where) s cmmi10.329 @sf 12 r m (A) s cmr10.329 @sf 11 r m (is) 12 (an) ks cmmi10.329 @sf 12 r m (n) s cmr10.329 @sf 12 r m (b) 0 (y) ks cmmi10.329 @sf 10 r m (m) s cmr10.329 @sf 11 r m (matrix,) s cmmi10.329 @sf 12 r m (B) s cmr10.329 @sf 14 r m (is) 12 (an) ks cmmi10.329 @sf 12 r m (n) s cmr10.329 @sf 12 r m (b) 0 (y) ks cmmi10.329 @sf 10 r m (p) s cmr10.329 @sf 11 r m (matrix.) 19 (Indeed,) 13 (the) 12 (QR) 12 (factorization) 11 (approac) 0 (hs) ks 60 102 p m (ha) 0 (v) -1 (e) 15 (b) 1 (een) 17 (used) 16 (for) 16 (solving) 16 (these) 16 (problems,) 17 (see) 16 (La) 0 (wson) 15 (and) 16 (Hanson) 16 ([) 0 (8) ks 1455 102 p m (],) 15 (P) 0 (aige[) 0 (10) ks 1662 102 p m (].) 22 (W) -3 (e) 15 (will) ks 60 158 p m (see) 12 (that) 11 (the) 13 (GQR) 12 (factorization) 12 (of) ks cmmi10.329 @sf 11 r m (A) s cmr10.329 @sf 12 r m (and) s cmmi10.329 @sf 12 r m (B) s cmr10.329 @sf 15 r m (pro) 0 (vides) 11 (an) 12 (uniform) 13 (approac) 0 (h) 10 (to) 11 (these) 13 (problems.) ks 60 214 p m (The) 15 (b) 1 (ene\014t) 17 (of) 15 (this) 15 (approac) 0 (h) 14 (is) 16 (threefold.) 21 (First,) 14 (it) 16 (uses) 15 (a) 15 (single) 17 (GQR) 15 (factorization) 15 (concept) ks 60 271 p m (to) 12 (solv) 0 (e) 12 (these) 13 (problems) 14 (directly) -3 (.) 20 (Second,) 13 (from) 13 (soft) -1 (w) -1 (are) 11 (dev) 0 (elopmen) 0 (t) 11 (p) 1 (oin) 0 (t) 13 (of) 12 (view,) 14 (it) 13 (allo) 0 (ws) ks 60 327 p m (us) 13 (to) 13 (dev) 0 (elop) 13 (one) 13 (subroutine) 15 (that) 12 (can) 13 (b) 1 (e) 14 (used) 14 (for) 13 (solving) 14 (these) 13 (problems.) 20 (Third,) 14 (as) 13 (the) 13 (QR) ks 60 384 p m (factorization) 13 (pro) 0 (vides) 13 (imp) 1 (ortan) 0 (t) 12 (information) 14 (of) 13 (conditioning) 16 (of) 13 (linear) 14 (least) 14 (square,) 13 (classical) ks 60 440 p m (linear) 13 (regression) 12 (mo) 1 (del,) 13 (w) 0 (e) 11 (will) 13 (sho) 0 (w) 11 (that) 11 (the) 12 (GQR) 12 (factorization) 12 (is) 12 (the) 12 (same.) 19 (The) 12 (condition) ks 60 497 p m (n) 0 (um) 0 (b) 1 (ers) 12 (of) 12 (these) 14 (problems) 14 (can) 13 (b) 1 (e) 14 (exploited) 15 (from) 12 (the) 14 (triangular) 13 (factors) 12 (of) 13 (the) 13 (factorization.) ks 131 561 p m (The) 18 (principl) 1 (e) 20 (concepts) 18 (ab) 1 (out) 18 (the) 19 (GQR) 18 (factorization) 18 (discussed) 20 (in) 19 (this) 18 (note) 18 (ha) 0 (v) 0 (e) 16 (b) 1 (een) ks 60 618 p m (presen) 0 (ted) 17 (in) 19 (P) 0 (aige's) 17 (w) 0 (ork) 16 (on) 18 (GQR[) 0 (10) ks 821 618 p m (].) 28 (Ho) 0 (w) -1 (ev) -1 (er,) 16 (from) 17 (general-purp) 1 (ose) 20 (soft) 0 (w) -2 (are) 16 (dev) 0 (elop-) ks 60 674 p m (men) 0 (t) 20 (p) 1 (oin) 0 (t) 22 (of) 21 (view,) 23 (w) 0 (e) 21 (will) 23 (tak) 0 (e) 20 (a) 21 (di\013eren) 0 (t) 21 (approac) 0 (h) 21 (for) 21 (the) 21 (GQR) 23 (factorization.) 39 (The) ks 60 731 p m (de\014nition) 16 (of) 13 (the) 14 (GQR) 14 (factorization) 14 (is) 14 (di\013eren) 0 (t) 14 (from) 13 (the) 14 (one) 14 (presen) 0 (ted) 13 (in) 15 (P) 0 (aige's) 12 (pap) 1 (er.) 20 (As) ks 60 787 p m (a) 14 (guidelin) 1 (e) 16 (of) 14 (the) 15 (dev) 0 (elopmen) 0 (t) 13 (of) 14 (the) 15 (GQR) 15 (factorization) 14 (for) 14 (LAP) -3 (A) 0 (CK) 13 (library) -3 (,) 14 (in) 16 (this) 14 (note,) ks 60 844 p m (w) 0 (e) 15 (consider) 18 (the) 17 (di\013eren) 0 (t) 16 (p) 1 (ossible) 18 (cases) 17 (of) 16 (the) 17 (factorizations) 16 (and) 17 (practical) 18 (implemen) 0 (tation) ks 60 900 p m (of) 15 (the) 15 (factorizations.) ks 131 965 p m (The) 16 (outline) 17 (of) 15 (this) 17 (LAP) -3 (A) 0 (CK) 14 (w) 0 (orking) 15 (note) 16 (is) 16 (as) 16 (follo) 0 (ws:) 20 (In) 16 (next) 16 (t) 0 (w) -1 (o) 14 (sections,) 16 (w) 0 (e) 15 (shall) ks 60 1021 p m (sho) 0 (w) 12 (ho) 0 (w) 12 (to) 13 (use) 15 (existing) 14 (QR) 15 (factorization) 13 (and) 14 (its) 14 (v) -2 (arian) 0 (ts) 12 (to) 13 (construct) 13 (the) 14 (GQR) 14 (factoriza-) ks 60 1078 p m (tion) 15 (with) 16 (or) 15 (without) 15 (piv) 0 (oting) 15 (strategies) 14 (of) 15 (t) 0 (w) -1 (o) 13 (matrices) ks cmmi10.329 @sf 15 r m (A) s cmr10.329 @sf 16 r m (and) s cmmi10.329 @sf 15 r m (B) s cmr10.329 @sf 18 r m (ha) 0 (ving) 14 (the) 16 (same) 15 (n) 0 (um) -1 (b) 1 (er) ks 60 1134 p m (of) 15 (ro) 0 (ws.) 20 (The) 16 (implemen) 0 (tation) 16 (details) 17 (of) 15 (the) 16 (di\013eren) 0 (t) 15 (factorizations) 16 (are) 15 (discussed) 18 (in) 16 (section) ks 60 1191 p m (4.) 26 (Then) 17 (w) 0 (e) 16 (sho) 0 (w) 16 (the) 17 (applications) 19 (of) 17 (the) 17 (GQR) 18 (factorization) 17 (in) 18 (solving) 18 (the) 18 (linear) 18 (equalit) 0 (y) ks 60 1247 p m (constrained) 21 (least) 21 (square) 21 (problem,) 22 (generalized) 23 (linear) 22 (mo) 1 (del) 21 (problem,) 23 (and) 21 (estimating) 21 (the) ks 60 1304 p m (conditioning) 17 (of) 15 (these) 15 (problems.) ks 131 1368 p m (Notations:) 19 (....) ks cmbx10.432 @sf 60 1520 p save [ 27 39 -3 0 34] 50 @pc restore 163 1520 p save [<00007FF003000003FFFE0F00001FFFFF1F00003FF007BF0000FF8001FF0001FE0000FF0003F800 00FF0007F00000FF000FF00000FF001FE00000FF001FE00000FF003FC00000FF003FC00000FF00 7FC00000FF007F8001FFFFF87F8001FFFFF8FF8001FFFFF8FF8000000000FF8000000000FF8000 000000FF8000000000FF8000000000FF8000000000FF8000000000FF80000000007F8000000000 7F80000007007FC0000007003FC0000007003FC000000F001FE000000F001FE000000F000FF000 001F0007F000003F0003F800003F0001FE0000FF0000FF8001FF00003FF00FFF00001FFFFF0F00 0003FFFC070000007FE00300> 45 41 -4 0 54] 71 @pc restore 54 r m (eneral) s save [ 15 43 -3 0 20] 105 @pc restore 20 r save [ 25 27 -2 0 31] 122 @pc restore 31 r m (e) -1 (d) ks 21 r save [<00000000780000000001FE0000000003FF0000000003FF8000000007FF8000000007FFC0000000 0FFFC00000000FFFC00000000FFFE00000000F81E00000001F00600000001E00600000FFFE0060 000FFFFE0000003FE07F800000FFC03FE00001FCC037F00003F8C063F80007F060C1FC000FF03F 81FE001FE01F00FF001FE00000FF003FC000007F803FC000007F807FC000007FC07F8000003FC0 7F8000003FC0FF8000003FE0FF8000003FE0FF8000003FE0FF8000003FE0FF8000003FE0FF8000 003FE0FF8000003FE0FF8000003FE0FF8000003FE0FF8000003FE07F8000003FC07F8000003FC0 7FC000007FC07FC000007FC03FC000007F803FC000007F801FE00000FF001FE00000FF000FF000 01FE0007F00001FC0003F80003F80001FC0007F000007F001FC000003FC07F80000007FFFC0000 0000FFE00000> 43 53 -4 12 52] 81 @pc restore 52 r m (R) s 23 r save [ 36 41 -3 0 43] 70 @pc restore 38 r m (actor) s save [ 15 43 -3 0 20] 105 @pc restore 20 r save [ 25 27 -2 0 31] 122 @pc restore 31 r m (at) s save [ 15 43 -3 0 20] 105 @pc restore 19 r m (on) s cmr10.329 @sf 60 1630 p m (In) 18 (this) 18 (section,) 18 (w) 0 (e) 16 (\014rst) 17 (in) 0 (tro) 1 (duce) 17 (the) 17 (GQR) 18 (factorization) 17 (of) ks cmmi10.329 @sf 17 r m (n) s cmr10.329 @sf 18 r m (b) 0 (y) ks cmmi10.329 @sf 16 r m (m) s cmr10.329 @sf 17 r m (matrix) s cmmi10.329 @sf 17 r m (A) s cmr10.329 @sf 18 r m (and) s cmmi10.329 @sf 17 r m (n) s cmr10.329 @sf 18 r m (b) 0 (y) ks cmmi10.329 @sf 16 r m (p) s cmr10.329 @sf 60 1686 p m (matrix) s cmmi10.329 @sf 16 r m (B) s cmr10.329 @sf 20 r m (when) s cmmi10.329 @sf 17 r m (n) s cmsy10.329 @sf 16 r save [ 26 36 -4 7 35] 21 @pc restore cmmi10.329 @sf 50 r m (m) s cmr10.329 @sf m (,) 17 (the) 17 (most) 16 (frequen) 0 (tly) 16 (o) 1 (ccurring) 18 (case.) 24 (Then) 18 (for) 16 (the) 17 (case) ks cmmi10.329 @sf 16 r m (n) s 16 r save [<000001C00000078000001E00000078000001E00000078000000E00000038000000F0000003C000 000F0000003C000000F0000000F00000003C0000000F00000003C0000000F0000000380000000E 0000000780000001E0000000780000001E0000000780000001C0> 26 26 -4 2 35] 60 @pc restore 51 r m (m) s cmr10.329 @sf m (,) 16 (w) 0 (e) ks 60 1743 p m (in) 0 (tro) 1 (duce) 15 (the) 15 (GR) 0 (Q) 15 (factorization) 15 (of) ks cmmi10.329 @sf 15 r m (A) s cmr10.329 @sf 15 r m (and) s cmmi10.329 @sf 15 r m (B) s cmr10.329 @sf 2 r m (.) s cmbx10.329 @sf 131 1867 p save [<0007FC0600003FFF8E0000FE01FE0003F000FE0007E0007E000FC0007E001F80007E003F00007E 003F00007E007F00007E007E00007E007E00007E00FE003FFFE0FE003FFFE0FE00000000FE0000 0000FE00000000FE00000000FE000000007E000006007E000006007F000006003F00000E003F00 000E001F80001E000FC0001E0007E0003E0003F000FE0000FE03DE00003FFF0E000007FC0200> 35 31 -3 0 41] 71 @pc restore 41 r save [<000000F0000001F8000003FC000007FE000007FE000007FF00000FFF00000F0700000E03001FFE 0300FFFF0001F81F8007F81FE00FD833F01F8FE1F83F87C1FC3F0000FC7F0000FE7E00007E7E00 007EFE00007FFE00007FFE00007FFE00007FFE00007FFE00007FFE00007FFE00007FFE00007F7E 00007E7F0000FE7F0000FE3F0000FC1F8001F81F8001F80FC003F007E007E001F81F8000FFFF00 001FF800> 32 40 -3 9 39] 81 @pc restore 39 r save [ 36 31 -2 0 39] 82 @pc restore 56 r m (factori) s save [ 19 20 -1 0 23] 122 @pc restore 23 r m (ation) s cmr10.329 @sf m (.) s cmti10.329 @sf 22 r save [ 25 31 -3 0 29] 76 @pc restore 28 r m (et) s cmmi10.329 @sf 14 r m (A) s cmti10.329 @sf 15 r m (b) -1 (e) 14 (an) ks cmmi10.329 @sf 15 r m (n) s cmti10.329 @sf 16 r m (b) s save [<3E0000438000C0C000E06000F07000F03800003800001C00001C0007DC000C3C001C1E00180E00 180E001C0E001C07001C07001C07001C07000E03800E03800E03808703804701C04301C04381C0 2301C03300E00E00C0> 19 29 -4 9 22] 121 @pc restore cmmi10.329 @sf 38 r m (m) s cmti10.329 @sf 15 r m (matrix,) s cmmi10.329 @sf 16 r m (B) s cmti10.329 @sf 19 r m (b) -1 (e) 14 (an) ks cmmi10.329 @sf 15 r m (n) s cmti10.329 @sf 16 r m (b) s save [<3E0000438000C0C000E06000F07000F03800003800001C00001C0007DC000C3C001C1E00180E00 180E001C0E001C07001C07001C07001C07000E03800E03800E03808703804701C04301C04381C0 2301C03300E00E00C0> 19 29 -4 9 22] 121 @pc restore cmmi10.329 @sf 37 r m (p) s cmti10.329 @sf 16 r m (matrix,) s cmmi10.329 @sf 16 r m (n) s cmsy10.329 @sf 13 r save [ 26 36 -4 7 35] 21 @pc restore cmmi10.329 @sf 48 r m (m) s cmti10.329 @sf m (,) 15 (then) ks 60 1924 p m (ther) -1 (e) 15 (ar) -1 (e) 15 (ortho) -1 (gonal) 16 (matric) -1 (es) ks cmmi10.329 @sf 15 r m (Q) s cmr10.329 @sf m (\() s cmmi10.329 @sf m (n) s cmsy10.329 @sf 10 r m (\002) s cmmi10.329 @sf 10 r m (n) s cmr10.329 @sf m (\)) s cmti10.329 @sf 17 r m (and) s cmmi10.329 @sf 16 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr10.329 @sf 36 r m (\() s cmmi10.329 @sf m (p) s cmsy10.329 @sf 10 r m (\002) s cmmi10.329 @sf 11 r m (p) s cmr10.329 @sf m (\)) s cmti10.329 @sf 15 r m (such) 17 (that) ks cmmi10.329 @sf 695 2026 p m (Q) s cmr8.300 @sf 731 2008 p m (T) s cmmi10.329 @sf 759 2026 p m (A) s cmr10.329 @sf 12 r m (=) s cmmi10.329 @sf 13 r m (R) 0 (;) 96 (Q) ks cmr8.300 @sf 1033 2008 p m (T) s cmmi10.329 @sf 1060 2026 p m (B) s 2 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr10.329 @sf 50 r m (=) s cmmi10.329 @sf 13 r m (S) s cmr10.329 @sf 1802 2026 p m (\(1\)) s cmti10.329 @sf 60 2128 p m (assumes) 16 (one) 16 (of) 16 (the) 17 (fol) 2 (lowing) 15 (forms) ks save [ 8 20 -5 0 14] 58 @pc restore 60 2185 p m (if) s cmmi10.329 @sf 16 r m (n) s cmsy10.329 @sf 13 r save [ 26 36 -4 7 35] 20 @pc restore cmmi10.329 @sf 48 r m (p) s cmti10.329 @sf m (,) s cmmi10.329 @sf 501 2272 p m (R) s cmr10.329 @sf 12 r m (=) s cmex10.300 @sf 625 2199 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 670 2245 p m (R) s cmr8.300 @sf 705 2252 p m (11) s cmr10.329 @sf 695 2299 p m (0) s cmex10.300 @sf 763 2199 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 796 2245 p m (m) s 796 2299 p m (n) s cmsy10.329 @sf 11 r m (\000) s cmmi10.329 @sf 10 r m (m) s 686 2362 p m (m) s 961 2299 p m (;) s 1039 2272 p m (S) s cmr10.329 @sf 16 r m (=) s cmex10.300 @sf 1162 2224 p m (h) s cmr10.329 @sf 1203 2272 p m (0) s cmmi10.329 @sf 1267 2272 p m (S) s cmr8.300 @sf 1295 2279 p m (11) s cmex10.300 @sf 1353 2224 p m (i) s cmmi10.329 @sf 1379 2272 p m (n) s 1180 2337 p m (p) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 11 r m (n) s 1327 2337 p m (n) s 1427 2299 p m (;) s cmti10.329 @sf 60 2441 p m (wher) -1 (e) ks cmmi10.329 @sf 15 r m (m) s cmti10.329 @sf 17 r m (b) s save [<3E0000438000C0C000E06000F07000F03800003800001C00001C0007DC000C3C001C1E00180E00 180E001C0E001C07001C07001C07001C07000E03800E03800E03808703804701C04301C04381C0 2301C03300E00E00C0> 19 29 -4 9 22] 121 @pc restore cmmi10.329 @sf 38 r m (m) s cmti10.329 @sf 16 r m (matrix) s cmmi10.329 @sf 17 r m (R) s cmr8.300 @sf 541 2448 p m (11) s cmti10.329 @sf 594 2441 p m (and) s cmmi10.329 @sf 16 r m (n) s cmti10.329 @sf 17 r m (b) s save [<3E0000438000C0C000E06000F07000F03800003800001C00001C0007DC000C3C001C1E00180E00 180E001C0E001C07001C07001C07001C07000E03800E03800E03808703804701C04301C04381C0 2301C03300E00E00C0> 19 29 -4 9 22] 121 @pc restore cmmi10.329 @sf 38 r m (n) s cmti10.329 @sf 17 r m (matrix) s cmmi10.329 @sf 17 r m (S) s cmr8.300 @sf 1003 2448 p m (11) s cmti10.329 @sf 1056 2441 p m (ar) -1 (e) 15 (upp) -1 (er) 16 (triangular,) 17 (and) 16 (if) ks cmmi10.329 @sf 16 r m (n) s 13 r save [ 26 26 -4 2 35] 62 @pc restore 48 r m (p) s cmti10.329 @sf m (,) s cmmi10.329 @sf 479 2575 p m (R) s cmr10.329 @sf 12 r m (=) s cmex10.300 @sf 603 2502 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 648 2547 p m (R) s cmr8.300 @sf 683 2554 p m (11) s cmr10.329 @sf 673 2602 p m (0) s cmex10.300 @sf 741 2502 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 774 2547 p m (m) s 774 2602 p m (n) s cmsy10.329 @sf 11 r m (\000) s cmmi10.329 @sf 10 r m (m) s 664 2664 p m (m) s 939 2602 p m (;) s 1017 2575 p m (S) s cmr10.329 @sf 16 r m (=) s cmex10.300 @sf 1137 2502 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 1182 2547 p m (S) s cmr8.300 @sf 1210 2554 p m (11) s cmmi10.329 @sf 1182 2602 p m (S) s cmr8.300 @sf 1210 2609 p m (21) s cmex10.300 @sf 1268 2502 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 1302 2547 p m (n) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 11 r m (p) s 1302 2602 p m (p) s 1204 2664 p m (p) s 1449 2602 p m (;) s @eop 2 @bop0 2 @bop1 cmsl10.329 @sf 60 -99 p m (The) 15 (Generalized) 17 (QR) 16 (Decomp) 1 (osition) ks cmr10.329 @sf 1059 r m (2) s 60 45 p m (whic) 0 (h) 17 (is) 17 (kno) 0 (wn) 16 (as) 17 (the) 17 (R) 0 (Q) 16 (factorization.) 25 (As) 17 (the) 17 (v) -2 (arian) 0 (ts) 15 (of) 17 (the) 17 (QR) 17 (and) 18 (R) 0 (Q) 16 (factorization) ks 60 102 p m (of) 15 (matrix) ks cmmi10.329 @sf 15 r m (A) s cmr10.329 @sf m (,) 15 (w) 0 (e) 14 (also) 16 (ha) 0 (v) -1 (e) 14 (QL) 16 (and) 16 (LQ) 16 (factorization,) 15 (whic) 0 (h) 15 (are) 15 (orthogonal-lo) 0 (w) -1 (er) 14 (triangular) ks 60 158 p m (and) 14 (lo) 0 (w) 0 (er) 12 (triangular-orthogonal) 14 (factorization,) 14 (resp) 1 (ectiv) 0 (ely) -3 (.) 19 (Moreo) 0 (v) -1 (er,) 12 (it) 14 (is) 15 (w) 0 (ell-kno) 0 (wn) 13 (that) ks 60 214 p m (the) 15 (orthogonal) 15 (factors) 14 (of) ks cmmi10.329 @sf 15 r m (A) s cmr10.329 @sf 15 r m (pro) 0 (vide) 15 (information) 15 (ab) 1 (out) 15 (its) 15 (column) 16 (and) 16 (ro) 0 (w) 13 (spaces) 15 ([) 0 (4) ks 1726 214 p m (].) s 131 279 p m (A) 12 (column) 13 (piv) 0 (oting) 12 (option) 13 (in) 13 (the) 12 (QR) 13 (factorization) 12 (allo) 0 (ws) 12 (the) 12 (user) 13 (to) 11 (detect) 13 (dep) 1 (endenci) 1 (es) ks 60 336 p m (among) 15 (the) 15 (columns) 16 (of) 15 (matrix) ks cmmi10.329 @sf 15 r m (A) s cmr10.329 @sf m (.) 20 (If) ks cmmi10.329 @sf 16 r m (A) s cmr10.329 @sf 15 r m (has) 16 (rank) ks cmmi10.329 @sf 15 r save [<600F00E01880701880703840703840703840381C203838003838003870001FC0001E00001D0000 1C80000E40600E20F00E10F00E08700706100701E0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 20 32 -2 0 24] 107 @pc restore cmr10.329 @sf 25 r m (,) 15 (then) 15 (there) 16 (are) 15 (orthogonal) 14 (matrix) ks cmmi10.329 @sf 15 r m (Q) s cmr10.329 @sf 16 r m (and) s 60 392 p m (a) 15 (p) 1 (erm) 0 (utation) 14 (matrix) ks cmmi10.329 @sf 15 r m (P) s cmr10.329 @sf 22 r m (suc) 0 (h) 14 (that) ks cmmi10.329 @sf 642 518 p m (Q) s cmr8.300 @sf 678 503 p m (T) s cmmi10.329 @sf 706 518 p m (AP) s cmr10.329 @sf 19 r m (=) s cmex10.300 @sf 865 445 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 910 491 p m (R) s cmr8.300 @sf 945 498 p m (11) s cmmi10.329 @sf 1023 491 p m (R) s cmr8.300 @sf 1058 498 p m (12) s cmr10.329 @sf 934 545 p m (0) s 1048 545 p m (0) s cmex10.300 @sf 1116 445 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 1149 491 p save [<600F00E01880701880703840703840703840381C203838003838003870001FC0001E00001D0000 1C80000E40600E20F00E10F00E08700706100701E0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 20 32 -2 0 24] 107 @pc restore 1149 545 p m (n) s cmsy10.329 @sf 11 r m (\000) s cmmi10.329 @sf 10 r save [<600F00E01880701880703840703840703840381C203838003838003870001FC0001E00001D0000 1C80000E40600E20F00E10F00E08700706100701E0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 20 32 -2 0 24] 107 @pc restore 909 607 p save [<600F00E01880701880703840703840703840381C203838003838003870001FC0001E00001D0000 1C80000E40600E20F00E10F00E08700706100701E0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 20 32 -2 0 24] 107 @pc restore 975 607 p m (m) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 11 r save [<600F00E01880701880703840703840703840381C203838003838003870001FC0001E00001D0000 1C80000E40600E20F00E10F00E08700706100701E0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 20 32 -2 0 24] 107 @pc restore cmr10.329 @sf 60 701 p m (where) s cmmi10.329 @sf 15 r m (R) s cmr8.300 @sf 226 708 p m (11) s cmr10.329 @sf 278 701 p m (is) 16 (a) ks cmmi10.329 @sf 15 r save [<600F00E01880701880703840703840703840381C203838003838003870001FC0001E00001D0000 1C80000E40600E20F00E10F00E08700706100701E0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 20 32 -2 0 24] 107 @pc restore cmr10.329 @sf 40 r m (b) 0 (y) ks cmmi10.329 @sf 14 r save [<600F00E01880701880703840703840703840381C203838003838003870001FC0001E00001D0000 1C80000E40600E20F00E10F00E08700706100701E0070000070000038000038000038000038000 01C00001C00001C00001C0000FE00001E000> 20 32 -2 0 24] 107 @pc restore cmr10.329 @sf 41 r m (upp) 1 (er) 16 (triangular) 15 (and) 16 (nonsingular[) 0 (4) ks 1202 701 p m (].) s 131 766 p m (Householder) 16 (transformation) 13 (matrix) 15 (or) 14 (Giv) 0 (ens) 15 (rotation) 14 (matrix) 15 (pro) 0 (vide) 14 (n) 0 (umerical) 16 (stable) ks 60 822 p m (n) 0 (umerical) 15 (metho) 1 (ds) 14 (to) 14 (compute) 14 (these) 14 (factorizations) 14 (with) 15 (or) 14 (without) 14 (piv) 0 (oting.) 19 (The) 15 (soft) 0 (w) -2 (are) ks 60 879 p m (for) 16 (computing) 18 (the) 17 (QR) 17 (factorization) 17 (on) 17 (sequen) 0 (tial) 17 (mac) 0 (hines) 17 (is) 17 (a) 0 (v) -2 (ailable) 17 (from) 16 (public) 19 (linear) ks 60 935 p m (algebra) 16 (library) 17 (LINP) -3 (A) 0 (CK[) 0 (7) ks 612 935 p m (].) 22 (Redesigned) 19 (co) 1 (des) 16 (in) 18 (blo) 1 (c) 0 (k) 16 (algorithm) 16 (fashion) 16 (that) 16 (are) 16 (b) 1 (etter) ks 60 992 p m (suited) 16 (for) 15 (to) 1 (da) 0 (y's) 13 (high-p) 1 (erformance) 16 (arc) 0 (hitectures) 15 (can) 15 (b) 1 (e) 16 (found) 15 (in) 16 (LAP) -3 (A) 0 (CK.) ks 131 1056 p m (The) 21 (terminology) ks cmti10.329 @sf 21 r m (gener) -1 (ali) ks save [<80E00041F80063FC003E0C00100200080200040100020000010000008000004000002000001000 0008000004000802000C1F0007F18003E08001C040> 18 20 -3 0 19] 122 @pc restore 18 r m (e) -2 (d) ks 20 r save [<0000F0000001F8000003FC000003FE000003860000038300000101000001018001FD0080074380 800E41E0001C41700038413C0038411E0070200F00701C070070000380F00003C0F00001C0F000 01E0F00000E0F00000F0F00000F0780000787800007878000078780000783C0000783C0000381E 0000381E0000380F00003807000038078000780380007001C0007000E000E0003000E0001C01C0 000707000001FC00> 29 41 -6 9 35] 81 @pc restore 35 r m (R) 21 (factori) ks save [<80E00041F80063FC003E0C00100200080200040100020000010000008000004000002000001000 0008000004000802000C1F0007F18003E08001C040> 18 20 -3 0 19] 122 @pc restore 19 r m (ations) s cmr10.329 @sf 21 r m (\(GQR) 21 (factorization\),) 21 (whic) 0 (h) 21 (has) 21 (b) 1 (een) ks 60 1113 p m (in) 0 (tro) 1 (duced) 18 (b) 0 (y) 16 (Hammarling[) 0 (6) ks 637 1113 p m (]) 17 (and) 18 (P) 0 (aige[) 0 (9) ks 901 1113 p m (],) 18 (is) 18 (to) 17 (refer) 18 (to) 17 (orthogonal) 16 (transformations) 17 (that) ks 60 1169 p m (apply) 19 (to) ks cmmi10.329 @sf 18 r m (n) s cmr10.329 @sf 19 r m (b) 0 (y) ks cmmi10.329 @sf 17 r m (m) s cmr10.329 @sf 18 r m (matrix) s cmmi10.329 @sf 19 r m (A) s cmr10.329 @sf 18 r m (and) s cmmi10.329 @sf 19 r m (n) s cmr10.329 @sf 18 r m (b) 0 (y) ks cmmi10.329 @sf 18 r m (p) s cmr10.329 @sf 18 r m (matrix) s cmmi10.329 @sf 18 r m (B) s cmr10.329 @sf 21 r m (to) 18 (transform) 17 (them) 19 (to) 17 (triangular) 19 (forms,) ks 60 1226 p m (resp) 1 (ectiv) 0 (ely) -3 (,) 15 (but) 15 (whic) 0 (h) 15 (corresp) 1 (onds) 16 (to) 15 (the) 15 (QR) 16 (factorization) 15 (of) ks cmmi10.329 @sf 15 r m (B) s cmsy8.300 @sf 1350 1211 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 1398 1226 p m (A) s cmr10.329 @sf 16 r m (in) 16 (the) 15 (case) 15 (whenev) 0 (er) ks cmmi10.329 @sf 60 1282 p m (B) s cmr10.329 @sf 18 r m (is) 15 (square) 15 (and) 15 (nonsingular.) 21 (F) -3 (or) 14 (example,) 15 (if) ks cmmi10.329 @sf 16 r m (n) s cmsy10.329 @sf 13 r save [ 26 36 -4 7 35] 21 @pc restore cmmi10.329 @sf 48 r m (m) s cmr10.329 @sf m (,) s cmmi10.329 @sf 14 r m (n) s cmsy10.329 @sf 13 r save [ 26 36 -4 7 35] 20 @pc restore cmmi10.329 @sf 48 r m (p) s cmr10.329 @sf m (,) 15 (then) 15 (the) 15 (GQR) 16 (factorization) 14 (of) ks cmmi10.329 @sf 60 1339 p m (A) s cmr10.329 @sf 15 r m (and) s cmmi10.329 @sf 16 r m (B) s cmr10.329 @sf 18 r m (assumes) 15 (the) 15 (form) ks cmmi10.329 @sf 589 1455 p m (Q) s cmr8.300 @sf 625 1437 p m (T) s cmmi10.329 @sf 653 1455 p m (A) s cmr10.329 @sf 12 r m (=) s cmex10.300 @sf 747 1383 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 792 1428 p m (R) s cmr10.329 @sf 798 1483 p m (0) s cmex10.300 @sf 848 1383 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 880 1455 p m (;) 45 (Q) ks cmr8.300 @sf 974 1437 p m (T) s cmmi10.329 @sf 1001 1455 p m (B) s 2 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr10.329 @sf 50 r m (=) s cmex10.300 @sf 1135 1408 p m (h) s cmr10.329 @sf 1176 1455 p m (0) s cmmi10.329 @sf 1240 1455 p m (S) s cmex10.300 @sf 1291 1408 p m (i) s cmmi10.329 @sf 1318 1455 p m (;) s cmr10.329 @sf 60 1579 p m (where) s cmmi10.329 @sf 16 r m (Q) s cmr10.329 @sf 17 r m (is) 16 (an) ks cmmi10.329 @sf 16 r m (n) s cmr10.329 @sf 17 r m (b) 0 (y) ks cmmi10.329 @sf 15 r m (n) s cmr10.329 @sf 16 r m (orthogonal) 16 (matrix,) ks cmmi10.329 @sf 16 r save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr10.329 @sf 52 r m (is) 17 (a) ks cmmi10.329 @sf 16 r m (p) s cmr10.329 @sf 16 r m (b) 0 (y) ks cmmi10.329 @sf 15 r m (p) s cmr10.329 @sf 16 r m (upp) 1 (er) 17 (triangular) 17 (matrix,) ks cmmi10.329 @sf 15 r m (R) s cmr10.329 @sf 16 r m (is) 17 (a) ks cmmi10.329 @sf 16 r m (m) s cmr10.329 @sf 60 1636 p m (b) 0 (y) ks cmmi10.329 @sf 13 r m (m) s cmr10.329 @sf 13 r m (upp) 1 (er) 15 (triangular,) ks cmmi10.329 @sf 14 r m (S) s cmr10.329 @sf 17 r m (is) 14 (a) ks cmmi10.329 @sf 13 r m (p) s cmr10.329 @sf 14 r m (b) 0 (y) ks cmmi10.329 @sf 13 r m (p) s cmr10.329 @sf 14 r m (upp) 1 (er) 14 (triangular.) 20 (If) ks cmmi10.329 @sf 14 r m (B) s cmr10.329 @sf 17 r m (is) 14 (square) 14 (and) 14 (nonsingular,) 15 (then) ks 60 1692 p m (the) 15 (QR) 16 (factorization) 15 (of) ks cmmi10.329 @sf 15 r m (B) s cmsy8.300 @sf 574 1677 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 622 1692 p m (A) s cmr10.329 @sf 15 r m (is) 16 (giv) 0 (en) 15 (b) 0 (y) ks cmmi10.329 @sf 614 1817 p save [<0080000000C0000001C0000001E0000001F0000001F0000001E8000001E8000001E4000001E200 0003E2000003C1000003C1800003C0800003C0400003C0400003C0200003C0100003C0100007C0 0800078008000780040007800200078002000780010007800080078000800F8000400F0000400F 0000600F800078FFF801FF> 32 32 -2 1 27] 86 @pc restore cmr8.300 @sf 651 1799 p m (T) s cmr10.329 @sf 678 1817 p m (\() s cmmi10.329 @sf m (B) s cmsy8.300 @sf 732 1799 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 780 1817 p m (A) s cmr10.329 @sf m (\)) 12 (=) ks cmex10.300 @sf 892 1745 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 937 1790 p save [<7FFFC00001F0000000F0000000F0000000F0000000F00000007800000078000000780000007800 00003C0000003C0000003C0000003C0000001E0000001E0000001E0000001E0000000F0000000F 0000000F0000800F0010400780084007800860078008200780082003C0081003C0081803C0181E 03C0380FFFFFFC> 30 31 -1 0 27] 84 @pc restore cmr10.329 @sf 942 1845 p m (0) s cmex10.300 @sf 991 1745 p save [ 12 124 0 122 24] 35 @pc restore cmr10.329 @sf 1028 1817 p m (=) s cmmi10.329 @sf 13 r m (S) s cmsy8.300 @sf 1107 1799 p m (\000) s cmr8.300 @sf m (1) s cmex10.300 @sf 1161 1745 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 1206 1790 p m (R) s cmr10.329 @sf 1212 1845 p m (0) s cmex10.300 @sf 1261 1745 p save [ 12 124 0 122 24] 35 @pc restore cmmi10.329 @sf 1293 1817 p m (;) s cmr10.329 @sf 60 1942 p m (i.e.,) 22 (the) 22 (upp) 1 (er) 22 (triangular) 21 (part) ks cmmi10.329 @sf 21 r save [<7FFFC00001F0000000F0000000F0000000F0000000F00000007800000078000000780000007800 00003C0000003C0000003C0000003C0000001E0000001E0000001E0000001E0000000F0000000F 0000000F0000800F0010400780084007800860078008200780082003C0081003C0081803C0181E 03C0380FFFFFFC> 30 31 -1 0 27] 84 @pc restore cmr10.329 @sf 54 r m (of) 20 (QR) 22 (factorization) 21 (can) 21 (b) 1 (e) 22 (determined) 23 (b) 0 (y) 20 (solving) 22 (the) ks 60 1999 p m (triangular) 15 (matrix) 15 (equation) ks cmmi10.329 @sf 874 2055 p m (S) s 3 r save [<7FFFC00001F0000000F0000000F0000000F0000000F00000007800000078000000780000007800 00003C0000003C0000003C0000003C0000001E0000001E0000001E0000001E0000000F0000000F 0000000F0000800F0010400780084007800860078008200780082003C0081003C0081803C0181E 03C0380FFFFFFC> 30 31 -1 0 27] 84 @pc restore cmr10.329 @sf 45 r m (=) s cmmi10.329 @sf 13 r m (R) 0 (:) ks cmr10.329 @sf 60 2135 p m (The) 17 (adv) -2 (an) 0 (tag) -1 (e) 15 (of) 17 (this) 17 (implici) 1 (t) 18 (determination) 18 (of) 16 (the) 17 (QR) 18 (factorization) 17 (of) ks cmmi10.329 @sf 16 r m (B) s cmsy8.300 @sf 1552 2120 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 1600 2135 p m (A) s cmr10.329 @sf 17 r m (is) 17 (ob) 0 (vious.) ks 60 2191 p m (W) -3 (e) 14 (a) 0 (v) -1 (oid) 14 (the) 16 (p) 1 (ossible) 16 (n) 0 (umerical) 16 (di) ks save [<7FE3FE3FF007007007000700700700070070070007007007000700700700070070070007007007 000700700700070070070007007007000700700700070070070007007007000700700700070070 0700070070070007007007000700700700FFFFFFFF000700700000070070000007007000000700 700000070070000007007000000700F00F000300F00F000380F80F0001C07C060000F04F040000 1F81F800> 36 32 0 0 38] 14 @pc restore 38 r m (culties) 17 (to) 15 (form) ks cmmi10.329 @sf 14 r m (B) s cmsy8.300 @sf 1132 2176 p m (\000) s cmr8.300 @sf m (1) s cmr10.329 @sf 1195 2191 p m (and) s cmmi10.329 @sf 16 r m (B) s cmsy8.300 @sf 1320 2176 p m (\000) s cmr8.300 @sf m (1) s cmmi10.329 @sf 1368 2191 p m (A) s cmr10.329 @sf m (.) s 131 2256 p m (As) 18 (the) 19 (p) 1 (o) 0 (w) -1 (erful) 18 (to) 1 (ol) 18 (of) 18 (QR) 19 (factorization) 19 (in) 19 (least) 19 (square) 18 (and) 19 (related) 19 (linear) 20 (regression) ks 60 2312 p m (problems,) 19 (as) 17 (examples,) 18 (w) 0 (e) 17 (shall) 19 (sho) 0 (w) 16 (that) 17 (the) 17 (GQR) 18 (factorization) 18 (can) 18 (b) 1 (een) 18 (used) 19 (to) 17 (solv) 0 (e) ks 60 2369 p m (linear) 16 (equalit) 0 (y) 15 (constrained) 16 (least) 15 (square) 16 (problem) ks 822 2464 p m (min) s cmmi8.300 @sf 813 2494 p m (B) 2 (x) ks cmr8.300 @sf m (=) s cmmi8.300 @sf save [<387046C8C1C480C480C480C0C060C060C06060606070307018F007300018001800180018000C00 0C000C000C003E> 15 23 -2 0 18] 100 @pc restore cmsy10.329 @sf 914 2464 p m (k) s cmmi10.329 @sf m (Ax) s cmsy10.329 @sf 10 r m (\000) s cmmi10.329 @sf 10 r m (b) s cmsy10.329 @sf m (k) s cmmi10.329 @sf m (;) s cmr10.329 @sf 60 2572 p m (where) s cmmi10.329 @sf 22 r m (A) s cmr10.329 @sf 22 r m (and) s cmmi10.329 @sf 22 r m (B) s cmr10.329 @sf 25 r m (are) s cmmi10.329 @sf 22 r m (m) s cmr10.329 @sf 22 r m (b) 0 (y) ks cmmi10.329 @sf 20 r m (n) s cmr10.329 @sf 23 r m (and) s cmmi10.329 @sf 22 r m (p) s cmr10.329 @sf 22 r m (b) 0 (y) ks cmmi10.329 @sf 21 r m (m) s cmr10.329 @sf 21 r m (matrices,) 24 (resp) 1 (ectiv) 0 (ely) -3 (,) 23 (and) 22 (generalized) 24 (linear) ks 60 2628 p m (regression) 15 (mo) 1 (del) ks 615 2685 p m (min) s cmmi8.300 @sf 627 2710 p m (x;u) s cmmi10.329 @sf 698 2685 p m (u) s cmr8.300 @sf 724 2667 p m (T) s cmmi10.329 @sf 752 2685 p m (u;) s cmr10.329 @sf 32 r m (sub) 3 (ject) 15 (to) ks cmmi10.329 @sf 1047 2685 p m (b) s cmr10.329 @sf 12 r m (=) s cmmi10.329 @sf 13 r m (Ax) s cmr10.329 @sf 10 r m (+) s cmmi10.329 @sf 11 r m (B) 2 (u) ks @eop 1 @bop0 1 @bop1 701 227 p save [ 25 34 -2 0 30] 76 @pc restore 30 r save [ 32 35 -2 0 37] 65 @pc restore 37 r save [ 27 34 -2 0 33] 80 @pc restore 30 r save [ 32 35 -2 0 37] 65 @pc restore 36 r save [<0007E00000381C0000E0020001C0010003800080070000400E0000401E0000201C0000203C0000 103C0000107C0000107800001078000000F8000000F8000000F8000000F8000000F8000000F800 0000F8000000F800000078000010780000107C0000103C0000303C0000301C0000301E0000700E 000070070000F0038000F001C0017000E00630003818300007E010> 28 36 -3 1 35] 67 @pc restore 35 r save [ 33 34 -2 0 38] 75 @pc restore 52 r save [<00020000800000030001800000070001C00000070001C00000070001C000000F8003E000000F80 03E000000F8003E000001E40079000001E40079000001E40079000003C200F0800003C200F0800 003C200F0800007C101E04000078101E04000078101E040000F8183E060000F0083C020000F008 3C020000F0083C020001E00478010001E00478010001E00478010003C002F0008003C002F00080 03C002F00080078001E00040078001E00040078001E000400F0003C000200F0003C000200F0003 C000701F8007E000F8FFF03FFC03FE> 47 35 -1 1 50] 87 @pc restore 47 r save [<01FC000707000E03801C01C03800E07800F0700070F00078F00078F00078F00078F00078F00078 F000787000707000703800E01800C00C018007070001FC00> 21 21 -1 0 24] 111 @pc restore 24 r save [ 16 21 -1 0 19] 114 @pc restore 19 r save [ 23 35 -1 0 26] 107 @pc restore 26 r save [ 10 34 -1 0 14] 105 @pc restore 14 r save [ 24 21 -1 0 27] 110 @pc restore 27 r save [<03FE000E03803800E0600030600030C00018C00018C000184000186000303800F00FFFE00FFFC0 1FFE0018000018000010000010000019F0000F1C000E0E001C07001C07003C07803C07803C0780 3C07801C07001C07000E0E18071E1801F198000070> 21 33 -1 11 24] 103 @pc restore 40 r save [ 32 34 -2 0 37] 78 @pc restore 37 r save [<01FC000707000E03801C01C03800E07800F0700070F00078F00078F00078F00078F00078F00078 F000787000707000703800E01800C00C018007070001FC00> 21 21 -1 0 24] 111 @pc restore 24 r save [<01F0030807080E040E040E040E040E040E040E000E000E000E000E000E000E000E000E000E000E 00FFF83E001E000E000600060006000200020002000200> 14 31 -1 0 19] 116 @pc restore 19 r save [<00FC000703000E00801C0040380020780020700000F00000F00000F00000F00000F00000FFFFE0 F000E07000E07801E03801C01C01C00C038007070001FC00> 19 21 -1 0 22] 101 @pc restore 221 319 p save [<00001FF000000000FFFE00800007F0078180000F8000C380003E00006380007C0000178000F000 00178001E000000F8003C000000F8007C000000F80078000000F800F0000000F801F0000000F80 1E0000000F803E0000000F803C0000000F803C0000000F807C0000000F807C0000001FC0780000 0FFFFCF800000FFFFCF80000000000F80000000000F80000000000F80000000000F80000000000 F80000000000F80000000000F80000000000F80000000000F800000000007800000000007C0000 0000807C00000000803C00000000803C00000001803E00000001801E00000001801F0000000180 0F000000038007800000038007800000078003C000000F8001E000000F8000F000001780007800 002780003E0000C380000F800183800007F00F01800000FFFC018000001FE00080> 46 51 -4 1 52] 71 @pc restore 52 r save [<001FC00000F0300001C00C00078002000F0002000E0001001E0000803C0000803C0000007C0000 0078000000F8000000F8000000F8000000F8000000F8000000F8000000FFFFFF80F8000780F800 07807800078078000F807C000F003C000F001C000F001E001E000E001E0007003C000380380000 E0E000003F8000> 25 31 -2 0 29] 101 @pc restore 29 r save [ 33 31 -2 0 37] 110 @pc restore 37 r save [<001FC00000F0300001C00C00078002000F0002000E0001001E0000803C0000803C0000007C0000 0078000000F8000000F8000000F8000000F8000000F8000000F8000000FFFFFF80F8000780F800 07807800078078000F807C000F003C000F001C000F001E001E000E001E0007003C000380380000 E0E000003F8000> 25 31 -2 0 29] 101 @pc restore 29 r save [ 22 31 -2 0 25] 114 @pc restore 25 r save [<03FC03E00F0307F03E008F087C005E0478003E04F8003E04F8003E04F8001E04F8001E04F8001E 047C001E003C001E003E001E001F001E000F801E0003E01E0000FC1E00000FFE0000001E000000 1E0000001E0008001E003E001E003E001E003E001C003C003C0010003800100070000C00E00003 03C00000FE0000> 30 31 -3 0 33] 97 @pc restore 33 r save [ 14 50 -2 0 18] 108 @pc restore 18 r save [ 13 48 -2 0 18] 105 @pc restore 18 r save [ 24 31 -2 0 29] 122 @pc restore 29 r save [<001FC00000F0300001C00C00078002000F0002000E0001001E0000803C0000803C0000007C0000 0078000000F8000000F8000000F8000000F8000000F8000000F8000000FFFFFF80F8000780F800 07807800078078000F807C000F003C000F001C000F001E001E000E001E0007003C000380380000 E0E000003F8000> 25 31 -2 0 29] 101 @pc restore 29 r save [<003F81FF00E061FF038011F0070009E00E0005E01E0003E01C0001E03C0001E03C0001E0780001 E0780001E0F80001E0F80001E0F80001E0F80001E0F80001E0F80001E0F80001E0F80001E0F800 01E0780001E07C0001E03C0001E03C0001E01E0001E00E0003E00F0003E0078005E001C019E000 F061E0001F81E0000001E0000001E0000001E0000001E0000001E0000001E0000001E0000001E0 000001E0000001E0000001E0000001E0000001E0000001E0000001E0000003E000003FE000003F E0000001E0> 32 50 -3 0 37] 100 @pc restore 59 r save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pc restore 52 r save [<000000000F80FFFF80003860FFFF8000701007F00000F01003E00001E00803E00001E00803E000 03E00803E00003E00803E00003E00003E00003E00003E00003E00003E00003E00003E00003E000 03E00003E00003E00003E00003E00003E00003E00003E00003E00003E00003E00003E00003E000 07C00003E00007800003E0000F800003E0001E000003E0007C000003E001F0000003FFFF000000 03E001F0000003E0003C000003E0000F000003E00007800003E00003C00003E00001E00003E000 01F00003E00000F00003E00000F80003E00000F80003E00000F80003E00000F80003E00000F800 03E00000F80003E00000F00003E00001F00003E00001E00003E00003E00003E00007C00003E000 0F800003E0003E000007E001FC0000FFFFFFF00000FFFFFF000000> 45 50 -4 1 49] 82 @pc restore 70 r save [ 36 49 -4 0 43] 70 @pc restore 38 r save [<03FC03E00F0307F03E008F087C005E0478003E04F8003E04F8003E04F8001E04F8001E04F8001E 047C001E003C001E003E001E001F001E000F801E0003E01E0000FC1E00000FFE0000001E000000 1E0000001E0008001E003E001E003E001E003E001C003C003C0010003800100070000C00E00003 03C00000FE0000> 30 31 -3 0 33] 97 @pc restore 33 r save [<003F8000E0600380180700040F00021E00021E00013C00017C00007C0000780000F80000F80000 F80000F80000F80000F80000F80000F80000F800007800007C00087C003E3C003E1C003E1E001E 0F000407000403801800E060003F80> 24 31 -3 0 29] 99 @pc restore 29 r save [<001F000078C000E04001E02001C02003C01003C01003C01003C01003C01003C01003C01003C010 03C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C000 03C00003C00003C000FFFFE01FFFE00FC00007C00003C00001C00001C00000C00000C00000C000 004000004000004000004000004000> 20 44 -1 0 25] 116 @pc restore 25 r save [<001FC00000F0780001C01C0007800F000F0007801E0003C01E0003C03C0001E03C0001E07C0001 F0780000F0F80000F8F80000F8F80000F8F80000F8F80000F8F80000F8F80000F8F80000F87800 00F0780000F0780000F03C0001E03C0001E01C0001C01E0003C00F0007800700070001C01C0000 F07800001FC000> 29 31 -2 0 33] 111 @pc restore 33 r save [ 22 31 -2 0 25] 114 @pc restore 25 r save [ 13 48 -2 0 18] 105 @pc restore 18 r save [ 24 31 -2 0 29] 122 @pc restore 29 r save [<03FC03E00F0307F03E008F087C005E0478003E04F8003E04F8003E04F8001E04F8001E04F8001E 047C001E003C001E003E001E001F001E000F801E0003E01E0000FC1E00000FFE0000001E000000 1E0000001E0008001E003E001E003E001E003E001C003C003C0010003800100070000C00E00003 03C00000FE0000> 30 31 -3 0 33] 97 @pc restore 33 r save [<001F000078C000E04001E02001C02003C01003C01003C01003C01003C01003C01003C01003C010 03C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C000 03C00003C00003C000FFFFE01FFFE00FC00007C00003C00001C00001C00000C00000C00000C000 004000004000004000004000004000> 20 44 -1 0 25] 116 @pc restore 25 r save [ 13 48 -2 0 18] 105 @pc restore 18 r save [<001FC00000F0780001C01C0007800F000F0007801E0003C01E0003C03C0001E03C0001E07C0001 F0780000F0F80000F8F80000F8F80000F8F80000F8F80000F8F80000F8F80000F8F80000F87800 00F0780000F0780000F03C0001E03C0001E01C0001C01E0003C00F0007800700070001C01C0000 F07800001FC000> 29 31 -2 0 33] 111 @pc restore 33 r save [ 33 31 -2 0 37] 110 @pc restore 59 r save [<03FC03E00F0307F03E008F087C005E0478003E04F8003E04F8003E04F8001E04F8001E04F8001E 047C001E003C001E003E001E001F001E000F801E0003E01E0000FC1E00000FFE0000001E000000 1E0000001E0008001E003E001E003E001E003E001C003C003C0010003800100070000C00E00003 03C00000FE0000> 30 31 -3 0 33] 97 @pc restore 33 r save [ 33 31 -2 0 37] 110 @pc restore 37 r save [<003F81FF00E061FF038011F0070009E00E0005E01E0003E01C0001E03C0001E03C0001E0780001 E0780001E0F80001E0F80001E0F80001E0F80001E0F80001E0F80001E0F80001E0F80001E0F800 01E0780001E07C0001E03C0001E03C0001E01E0001E00E0003E00F0003E0078005E001C019E000 F061E0001F81E0000001E0000001E0000001E0000001E0000001E0000001E0000001E0000001E0 000001E0000001E0000001E0000001E0000001E0000001E0000001E0000003E000003FE000003F E0000001E0> 32 50 -3 0 37] 100 @pc restore 58 r save [ 13 48 -2 0 18] 105 @pc restore 18 r save [<001F000078C000E04001E02001C02003C01003C01003C01003C01003C01003C01003C01003C010 03C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C000 03C00003C00003C000FFFFE01FFFE00FC00007C00003C00001C00001C00000C00000C00000C000 004000004000004000004000004000> 20 44 -1 0 25] 116 @pc restore 25 r save [<80FE00C301C0CC0060F00030F00038E00018E0001CC0001CC0001C80001C80003C80003C0000F8 0001F8003FF003FFE00FFFC01FFF003FF0007E0000F80000F00010E00010E00010E00010E00030 6000303000701800F00E033001FC10> 22 31 -2 0 26] 115 @pc restore 47 r save [ 46 50 -2 0 50] 65 @pc restore 50 r save [ 32 45 -2 14 37] 112 @pc restore 37 r save [ 32 45 -2 14 37] 112 @pc restore 37 r save [ 14 50 -2 0 18] 108 @pc restore 18 r save [ 13 48 -2 0 18] 105 @pc restore 18 r save [<003F8000E0600380180700040F00021E00021E00013C00017C00007C0000780000F80000F80000 F80000F80000F80000F80000F80000F80000F800007800007C00087C003E3C003E1C003E1E001E 0F000407000403801800E060003F80> 24 31 -3 0 29] 99 @pc restore 29 r save [<03FC03E00F0307F03E008F087C005E0478003E04F8003E04F8003E04F8001E04F8001E04F8001E 047C001E003C001E003E001E001F001E000F801E0003E01E0000FC1E00000FFE0000001E000000 1E0000001E0008001E003E001E003E001E003E001C003C003C0010003800100070000C00E00003 03C00000FE0000> 30 31 -3 0 33] 97 @pc restore 33 r save [<001F000078C000E04001E02001C02003C01003C01003C01003C01003C01003C01003C01003C010 03C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C000 03C00003C00003C000FFFFE01FFFE00FC00007C00003C00001C00001C00000C00000C00000C000 004000004000004000004000004000> 20 44 -1 0 25] 116 @pc restore 25 r save [ 13 48 -2 0 18] 105 @pc restore 18 r save [<001FC00000F0780001C01C0007800F000F0007801E0003C01E0003C03C0001E03C0001E07C0001 F0780000F0F80000F8F80000F8F80000F8F80000F8F80000F8F80000F8F80000F8F80000F87800 00F0780000F0780000F03C0001E03C0001E01C0001C01E0003C00F0007800700070001C01C0000 F07800001FC000> 29 31 -2 0 33] 111 @pc restore 33 r save [ 33 31 -2 0 37] 110 @pc restore 37 r save [<80FE00C301C0CC0060F00030F00038E00018E0001CC0001CC0001C80001C80003C80003C0000F8 0001F8003FF003FFE00FFFC01FFF003FF0007E0000F80000F00010E00010E00010E00010E00030 6000303000701800F00E033001FC10> 22 31 -2 0 26] 115 @pc restore 1699 294 p save [<00C00000C00000C00000C00000C000C0C0C0F0C3C038C7000EDC0003F00000C00003F0000EDC00 38C700F0C3C0C0C0C000C00000C00000C00000C00000C000> 18 21 -3 -2 25] 3 @pc restore 778 410 p save [<00020004000800100030006000C000C0018001800300070006000E000E000C001C001C00180038 0038003800700070007000700070007000F000F000E000E000E000E000E000E000E000E000E000 E000E000E000E000F000F00070007000700070007000700038003800380018001C001C000C000E 000E000600070003000180018000C000C0006000300010000800040002> 15 73 -6 19 25] 40 @pc restore 25 r save [<001800180000180018000018001800003C003C00003C003C00003C003C00003E007C00007A007A 00007A007A00007900FA0000F100F10000F100F10000F100F10001E081E08001E081E08001E081 E08003E043C04003C043C04003C043C04003C02780400780278020078027802007801F00200F00 1F00100F001F00100F001F00101E001E00181F001F003CFFE0FFE0FF> 40 29 -1 1 43] 87 @pc restore 41 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [ 19 29 -1 0 22] 107 @pc restore 34 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 20 18 -1 0 23] 110 @pc restore 36 r save [ 23 28 -2 0 28] 80 @pc restore 28 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<07F8001C0E00300300600180C000C0C000C0C000C06001C03003801FFF801FFF001FF800180000 30000010000013C0000C30001C3800181800381C00381C00381C00381C001818001C38800C38C0 03C4C0000380> 18 28 -1 9 21] 103 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<800040002000100018000C000600060003000300018001C000C000E000E0006000700070003000 3800380038001C001C001C001C001C001C001E001E000E000E000E000E000E000E000E000E000E 000E000E000E000E001E001E001C001C001C001C001C001C003800380038003000700070006000 E000E000C001C0018003000300060006000C0018001000200040008000> 15 73 -4 19 25] 41 @pc restore 564 569 p save [ 29 34 -2 0 33] 69 @pc restore 33 r save [<70F8F8F870> 5 5 -4 0 14] 46 @pc restore 30 r save [ 32 35 -2 0 37] 65 @pc restore 37 r save [ 24 21 -1 0 27] 110 @pc restore 27 r save [<01F0FE070CF00C02E01801E03800E07800E07000E0F000E0F000E0F000E0F000E0F000E0F000E0 F000E07000E07800E03800E01C01E00C02E00704E001F8E00000E00000E00000E00000E00000E0 0000E00000E00000E00000E00000E00000E00001E0000FE00000E0> 23 35 -2 0 27] 100 @pc restore 27 r save [<00FC000703000E00801C0040380020780020700000F00000F00000F00000F00000F00000FFFFE0 F000E07000E07801E03801C01C01C00C038007070001FC00> 19 21 -1 0 22] 101 @pc restore 22 r save [ 16 21 -1 0 19] 114 @pc restore 19 r save [<8FC0D030E018C008C00C800C800C801C003C01F80FF03FE07F80F000E008C008C008C018601830 780F88> 14 21 -2 0 19] 115 @pc restore 19 r save [<01FC000707000E03801C01C03800E07800F0700070F00078F00078F00078F00078F00078F00078 F000787000707000703800E01800C00C018007070001FC00> 21 21 -1 0 24] 111 @pc restore 24 r save [ 24 21 -1 0 27] 110 @pc restore 27 r save [<4020101008080404040474FCFCF870> 6 15 -4 10 14] 44 @pc restore 29 r save [ 24 34 -3 0 30] 90 @pc restore 30 r save [<70F8F8F870> 5 5 -4 0 14] 46 @pc restore 30 r save [ 29 34 -2 0 35] 66 @pc restore 35 r save [<0FC1E03C2390781708F00F08F00708F00708F007087007007807003C07001E070007C70000FF00 0007000007000007001807003C0E003C0C001838000FE000> 21 21 -2 0 24] 97 @pc restore 24 r save [ 10 34 -1 0 14] 105 @pc restore 30 r save [<0FC1E03C2390781708F00F08F00708F00708F007087007007807003C07001E070007C70000FF00 0007000007000007001807003C0E003C0C001838000FE000> 21 21 -2 0 24] 97 @pc restore 24 r save [ 24 21 -1 0 27] 110 @pc restore 27 r save [<01F0FE070CF00C02E01801E03800E07800E07000E0F000E0F000E0F000E0F000E0F000E0F000E0 F000E07000E07800E03800E01C01E00C02E00704E001F8E00000E00000E00000E00000E00000E0 0000E00000E00000E00000E00000E00000E00001E0000FE00000E0> 23 35 -2 0 27] 100 @pc restore 44 r save [<07C000187000203800401C00F01E00F80E00F80F00F80F00700F00000F00000F00000F00000F00 000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00 000F00000F00000F00000F00000F00000F00000F00001F0003FFF0> 20 35 -2 1 25] 74 @pc restore 25 r save [<70F8F8F870> 5 5 -4 0 14] 46 @pc restore 30 r save [ 31 34 -2 0 37] 68 @pc restore 37 r save [<01FC000707000E03801C01C03800E07800F0700070F00078F00078F00078F00078F00078F00078 F000787000707000703800E01800C00C018007070001FC00> 21 21 -1 0 24] 111 @pc restore 24 r save [ 24 21 -1 0 27] 110 @pc restore 27 r save [<03FE000E03803800E0600030600030C00018C00018C000184000186000303800F00FFFE00FFFC0 1FFE0018000018000010000010000019F0000F1C000E0E001C07001C07003C07803C07803C0780 3C07801C07001C07000E0E18071E1801F198000070> 21 33 -1 11 24] 103 @pc restore 24 r save [<0FC1E03C2390781708F00F08F00708F00708F007087007007807003C07001E070007C70000FF00 0007000007000007001807003C0E003C0C001838000FE000> 21 21 -2 0 24] 97 @pc restore 24 r save [ 16 21 -1 0 19] 114 @pc restore 19 r save [ 16 21 -1 0 19] 114 @pc restore 19 r save [<0FC1E03C2390781708F00F08F00708F00708F007087007007807003C07001E070007C70000FF00 0007000007000007001807003C0E003C0C001838000FE000> 21 21 -2 0 24] 97 @pc restore 771 680 p save [ 31 34 -2 0 37] 68 @pc restore 37 r save [<00FC000703000E00801C0040380020780020700000F00000F00000F00000F00000F00000FFFFE0 F000E07000E07801E03801C01C01C00C038007070001FC00> 19 21 -1 0 22] 101 @pc restore 22 r save [<01F8000706000C01001C0080380040780040700000F00000F00000F00000F00000F00000F00000 F000007000007800003803001C07800C078007030001FE00> 18 21 -2 0 22] 99 @pc restore 22 r save [<00FC000703000E00801C0040380020780020700000F00000F00000F00000F00000F00000FFFFE0 F000E07000E07801E03801C01C01C00C038007070001FC00> 19 21 -1 0 22] 101 @pc restore 22 r save [ 39 21 -1 0 42] 109 @pc restore 40 r save [<083F000C41C00C80600F00700E00380E003C0E001C0E001E0E001E0E001E0E001E0E001E0E001E 0E001E0E001C0E003C0E00380F00300E80600E61C00E1F000E00000E00000E00000E00000E0000 0E00000E00000E00000E00000E00000E00001E0000FE00000E0000> 23 35 -1 0 27] 98 @pc restore 28 r save [<00FC000703000E00801C0040380020780020700000F00000F00000F00000F00000F00000FFFFE0 F000E07000E07801E03801C01C01C00C038007070001FC00> 19 21 -1 0 22] 101 @pc restore 22 r save [ 16 21 -1 0 19] 114 @pc restore 34 r save [<0FC000103000201800700C007806007807003003000003800003800001C00001C00001C003E1E0 0619E00C05E01805E03803E07003E07001E0F001E0F001E0F001E0F001E0F001E0F001C0F001C0 F001C07003807003803803801807000C0600060C0001F000> 19 34 -2 1 24] 57 @pc restore 24 r save [<4020101008080404040474FCFCF870> 6 15 -4 10 14] 44 @pc restore 30 r save [ 15 33 -4 0 24] 49 @pc restore 24 r save [<0FC000103000201800700C007806007807003003000003800003800001C00001C00001C003E1E0 0619E00C05E01805E03803E07003E07001E0F001E0F001E0F001E0F001E0F001E0F001C0F001C0 F001C07003807003803803801807000C0600060C0001F000> 19 34 -2 1 24] 57 @pc restore 24 r save [<0FC000103000201800700C007806007807003003000003800003800001C00001C00001C003E1E0 0619E00C05E01805E03803E07003E07001E0F001E0F001E0F001E0F001E0F001E0F001C0F001C0 F001C07003807003803803801807000C0600060C0001F000> 19 34 -2 1 24] 57 @pc restore 24 r save [ 15 33 -4 0 24] 49 @pc restore 869 847 p save [ 31 28 -2 0 36] 65 @pc restore 36 r save [<1C3F001EC1E01F80701F00781F003C1F003C1F003E1F003E1F003E1F003E1F003E1F003E1F003C 1F003C1F00781F80701FE1E01F3F801F00001F00001F00001F00001F00001F00001F00001F0000 1F0000FF0000FF0000> 23 29 -1 0 27] 98 @pc restore 27 r save [ 14 18 -2 0 19] 115 @pc restore 19 r save [<03F007980F081F0C1F0C1F0C1F0C1F001F001F001F001F001F001F001F001F00FFFC3FFC0F000F 00070007000300030003000300> 14 26 -1 0 19] 116 @pc restore 19 r save [ 17 18 -1 0 20] 114 @pc restore 20 r save [<0FE1F83E13F8780BC0F807C0F807C0F807C07C07C03C07C01F07C007E7C0007FC00007C01C07C0 3E07C03E07803E0F801C1E000FF800> 21 18 -1 0 23] 97 @pc restore 23 r save [<03F8000E0E001C03003C0180780180780000F80000F80000F80000F80000F80000F80000780E00 781F003C1F001C1F000E0E0003FC00> 17 18 -2 0 21] 99 @pc restore 21 r save [<03F007980F081F0C1F0C1F0C1F0C1F001F001F001F001F001F001F001F001F00FFFC3FFC0F000F 00070007000300030003000300> 14 26 -1 0 19] 116 @pc restore 236 923 p save [<03FFFC00001F8000000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F00 00000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F0000800F 0020800F0020800F0020C00F0020400F0040400F0040600F00C0700F01C07FFFFFC0> 27 28 -1 0 30] 84 @pc restore 30 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 35 r save [ 19 26 -1 8 23] 112 @pc restore 23 r save [<03E3F00E1B800C07801C07801C03801C03801C03801C03801C03801C03801C03801C03801C0380 1C03801C03801C03801C0380FC1F80> 20 18 -1 0 23] 117 @pc restore 23 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [ 19 26 -1 8 23] 112 @pc restore 24 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 37 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00E000E 000E000E000E000E000E0C061E071E018C00F8> 15 29 0 0 13] 102 @pc restore 29 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 33 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 36 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 33 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 38 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 11 2 0 -8 14] 45 @pc restore 14 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 22 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 23 r save [<03E3F00E1B800C07801C07801C03801C03801C03801C03801C03801C03801C03801C03801C0380 1C03801C03801C03801C0380FC1F80> 20 18 -1 0 23] 117 @pc restore 23 r save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 18 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 35 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 36 r save [<07F8001C0E00300300600180C000C0C000C0C000C06001C03003801FFF801FFF001FF800180000 30000010000013C0000C30001C3800181800381C00381C00381C00381C001818001C38800C38C0 03C4C0000380> 18 28 -1 9 21] 103 @pc restore 21 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 14 18 -1 0 18] 122 @pc restore 18 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 40 r save [<00000F0000001F8000003FC000003FC0000038E00000306000006020003FE02000F0E02003A078 0007205C000E208E001C1107003C0E078038000380780003C0780003C0700001C0F00001E0F000 01E0F00001E0F00001E0F00001E0F00001E0F00001E0F00001E0700001C0780003C0780003C038 0003803C0007801C0007000E000E0007001C000380380000E0E000003F8000> 27 37 -2 8 32] 81 @pc restore 32 r save [<000007C0FFF01C200F003C200F0038100F0078100F0078100F0078000F0078000F0078000F0078 000F0078000F0078000F00F0000F00E0000F03C0000FFF00000F01E0000F0078000F003C000F00 1C000F001E000F001E000F001E000F001E000F001C000F003C000F0078000F01E000FFFF0000> 28 29 -2 1 31] 82 @pc restore 48 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00E000E 000E000E000E000E000E0C061E071E018C00F8> 15 29 0 0 13] 102 @pc restore 13 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 18 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 14 18 -1 0 18] 122 @pc restore 18 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 40 r save [<008020000180300001C0700001C0700003C0680003A0E80003A0E8000720C4000711C4000711C4 000E1182000E0B82000E0B82001C0B01001C0701001C0701803C0F0380FF3FCFE0> 27 18 -1 0 30] 119 @pc restore 30 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 20 29 -1 0 23] 104 @pc restore 174 973 p save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 33 r save [<008020000180300001C0700001C0700003C0680003A0E80003A0E8000720C4000711C4000711C4 000E1182000E0B82000E0B82001C0B01001C0701001C0701803C0F0380FF3FCFE0> 27 18 -1 0 30] 119 @pc restore 30 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<03E3F00E1B800C07801C07801C03801C03801C03801C03801C03801C03801C03801C03801C0380 1C03801C03801C03801C0380FC1F80> 20 18 -1 0 23] 117 @pc restore 23 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 34 r save [ 19 26 -1 8 23] 112 @pc restore 23 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<00400000E00000E00000E00001D00001D00003D8000388000388000704000704000704000E0200 0E02001C01001C01003C0380FF07E0> 19 18 -1 0 22] 118 @pc restore 22 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 11 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<07F8001C0E00300300600180C000C0C000C0C000C06001C03003801FFF801FFF001FF800180000 30000010000013C0000C30001C3800181800381C00381C00381C00381C001818001C38800C38C0 03C4C0000380> 18 28 -1 9 21] 103 @pc restore 37 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00E000E 000E000E000E000E000E0C061E071E018C00F8> 15 29 0 0 13] 102 @pc restore 30 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [<008020000180300001C0700001C0700003C0680003A0E80003A0E8000720C4000711C4000711C4 000E1182000E0B82000E0B82001C0B01001C0701001C0701803C0F0380FF3FCFE0> 27 18 -1 0 30] 119 @pc restore 30 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 36 r save [ 33 18 -1 0 36] 109 @pc restore 36 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 18 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 34 r save [ 28 29 -1 0 31] 65 @pc restore 48 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 41 r save [ 28 28 -2 0 31] 66 @pc restore 51 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<00400000E00000E00000E00001D00001D00003D8000388000388000704000704000704000E0200 0E02001C01001C01003C0380FF07E0> 19 18 -1 0 22] 118 @pc restore 22 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<07F8001C0E00300300600180C000C0C000C0C000C06001C03003801FFF801FFF001FF800180000 30000010000013C0000C30001C3800181800381C00381C00381C00381C001818001C38800C38C0 03C4C0000380> 18 28 -1 9 21] 103 @pc restore 37 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 36 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 33 18 -1 0 36] 109 @pc restore 36 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 35 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<03E3F00E1B800C07801C07801C03801C03801C03801C03801C03801C03801C03801C03801C0380 1C03801C03801C03801C0380FC1F80> 20 18 -1 0 23] 117 @pc restore 23 r save [ 33 18 -1 0 36] 109 @pc restore 34 r save [<10F8001906001E03001C01801C01C01C00C01C00E01C00E01C00E01C00E01C00E01C00E01C00C0 1C01C01C01801E03001D86001C7C001C00001C00001C00001C00001C00001C00001C00001C0000 1C00001C0000FC0000> 19 29 -1 0 23] 98 @pc restore 24 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 13 18 -1 0 16] 114 @pc restore 33 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00E000E 000E000E000E000E000E0C061E071E018C00F8> 15 29 0 0 13] 102 @pc restore 30 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<008020000180300001C0700001C0700003C0680003A0E80003A0E8000720C4000711C4000711C4 000E1182000E0B82000E0B82001C0B01001C0701001C0701803C0F0380FF3FCFE0> 27 18 -1 0 30] 119 @pc restore 30 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<804020201010101070F0F060> 4 12 -4 8 12] 44 @pc restore 29 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 174 1023 p save [<008020000180300001C0700001C0700003C0680003A0E80003A0E8000720C4000711C4000711C4 000E1182000E0B82000E0B82001C0B01001C0701001C0701803C0F0380FF3FCFE0> 27 18 -1 0 30] 119 @pc restore 30 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<00400000E00000E00000E00001D00001D00003D8000388000388000704000704000704000E0200 0E02001C01001C01003C0380FF07E0> 19 18 -1 0 22] 118 @pc restore 22 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 13 18 -1 0 16] 114 @pc restore 29 r save [ 28 28 -2 0 31] 66 @pc restore 46 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 29 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<003FE000070000070000070000070000070000070000070007C7000C3700180F00300F00700700 600700E00700E00700E00700E00700E00700E00700700700700700300F00180B000C330003C100> 19 26 -2 8 22] 113 @pc restore 22 r save [<03E3F00E1B800C07801C07801C03801C03801C03801C03801C03801C03801C03801C03801C0380 1C03801C03801C03801C0380FC1F80> 20 18 -1 0 23] 117 @pc restore 23 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 32 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 35 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<07F8001C0E00300300600180C000C0C000C0C000C06001C03003801FFF801FFF001FF800180000 30000010000013C0000C30001C3800181800381C00381C00381C00381C001818001C38800C38C0 03C4C0000380> 18 28 -1 9 21] 103 @pc restore 21 r save [<03E3F00E1B800C07801C07801C03801C03801C03801C03801C03801C03801C03801C03801C0380 1C03801C03801C03801C0380FC1F80> 20 18 -1 0 23] 117 @pc restore 23 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<804020201010101070F0F060> 4 12 -4 8 12] 44 @pc restore 24 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 32 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00E000E 000E000E000E000E000E0C061E071E018C00F8> 15 29 0 0 13] 102 @pc restore 13 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 18 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 14 18 -1 0 18] 122 @pc restore 18 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 35 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 33 18 -1 0 36] 109 @pc restore 36 r save [ 19 26 -1 8 23] 112 @pc restore 23 r save [ 9 29 -1 0 12] 108 @pc restore 11 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 18 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [<3C0000660000F30000F10000F0800000800000800000400000400000E00000E00000E00001D000 01D00003D8000388000388000704000704000704000E02000E02001C01001C01003C0380FF07E0> 19 26 -1 8 22] 121 @pc restore 32 r save [<07F8001C0E00300300600180C000C0C000C0C000C06001C03003801FFF801FFF001FF800180000 30000010000013C0000C30001C3800181800381C00381C00381C00381C001818001C38800C38C0 03C4C0000380> 18 28 -1 9 21] 103 @pc restore 21 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<00400000E00000E00000E00001D00001D00003D8000388000388000704000704000704000E0200 0E02001C01001C01003C0380FF07E0> 19 18 -1 0 22] 118 @pc restore 22 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 28 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 31 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<07F8001C0E00300300600180C000C0C000C0C000C06001C03003801FFF801FFF001FF800180000 30000010000013C0000C30001C3800181800381C00381C00381C00381C001818001C38800C38C0 03C4C0000380> 18 28 -1 9 21] 103 @pc restore 21 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 9 29 -1 0 12] 108 @pc restore 174 1073 p save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00E000E 000E000E000E000E000E0C061E071E018C00F8> 15 29 0 0 13] 102 @pc restore 13 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 18 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 14 18 -1 0 18] 122 @pc restore 18 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 41 r save [<008020000180300001C0700001C0700003C0680003A0E80003A0E8000720C4000711C4000711C4 000E1182000E0B82000E0B82001C0B01001C0701001C0701803C0F0380FF3FCFE0> 27 18 -1 0 30] 119 @pc restore 30 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 20 29 -1 0 23] 104 @pc restore 42 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 35 r save [<008020000180300001C0700001C0700003C0680003A0E80003A0E8000720C4000711C4000711C4 000E1182000E0B82000E0B82001C0B01001C0701001C0701803C0F0380FF3FCFE0> 27 18 -1 0 30] 119 @pc restore 30 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<03E3F00E1B800C07801C07801C03801C03801C03801C03801C03801C03801C03801C03801C0380 1C03801C03801C03801C0380FC1F80> 20 18 -1 0 23] 117 @pc restore 23 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 35 r save [ 19 26 -1 8 23] 112 @pc restore 23 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<00400000E00000E00000E00001D00001D00003D8000388000388000704000704000704000E0200 0E02001C01001C01003C0380FF07E0> 19 18 -1 0 22] 118 @pc restore 22 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 11 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<07F8001C0E00300300600180C000C0C000C0C000C06001C03003801FFF801FFF001FF800180000 30000010000013C0000C30001C3800181800381C00381C00381C00381C001818001C38800C38C0 03C4C0000380> 18 28 -1 9 21] 103 @pc restore 38 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00E000E 000E000E000E000E000E0C061E071E018C00F8> 15 29 0 0 13] 102 @pc restore 32 r save [ 28 28 -2 0 31] 66 @pc restore 988 1059 p save [ 18 2 -3 -6 26] 0 @pc restore 26 r save [ 10 19 -3 0 17] 49 @pc restore 1033 1073 p save [ 28 29 -1 0 31] 65 @pc restore 31 r save [<60F0F060> 4 4 -4 0 12] 46 @pc restore 46 r save [<03FFFC00001F8000000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F00 00000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F0000800F 0020800F0020800F0020C00F0020400F0040400F0040600F00C0700F01C07FFFFFC0> 27 28 -1 0 30] 84 @pc restore 30 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 37 r save [<001F800000E060800180118007000B800E0007801C0007801C0007803800078078000780780007 8070000780F0000F80F000FFF0F0000000F0000000F0000000F0000000F0000000F00000007000 00807800008078000080380001801C0001801C0003800E000380070007800180198000E0618000 1F8080> 28 30 -2 1 33] 71 @pc restore 33 r save [<00000F0000001F8000003FC000003FC0000038E00000306000006020003FE02000F0E02003A078 0007205C000E208E001C1107003C0E078038000380780003C0780003C0700001C0F00001E0F000 01E0F00001E0F00001E0F00001E0F00001E0F00001E0F00001E0700001C0780003C0780003C038 0003803C0007801C0007000E000E0007001C000380380000E0E000003F8000> 27 37 -2 8 32] 81 @pc restore 32 r save [<000007C0FFF01C200F003C200F0038100F0078100F0078100F0078000F0078000F0078000F0078 000F0078000F0078000F00F0000F00E0000F03C0000FFF00000F01E0000F0078000F003C000F00 1C000F001E000F001E000F001E000F001E000F001C000F003C000F0078000F01E000FFFF0000> 28 29 -2 1 31] 82 @pc restore 50 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00E000E 000E000E000E000E000E0C061E071E018C00F8> 15 29 0 0 13] 102 @pc restore 13 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 18 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 14 18 -1 0 18] 122 @pc restore 18 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 41 r save [<008020000180300001C0700001C0700003C0680003A0E80003A0E8000720C4000711C4000711C4 000E1182000E0B82000E0B82001C0B01001C0701001C0701803C0F0380FF3FCFE0> 27 18 -1 0 30] 119 @pc restore 30 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 34 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 11 2 0 -8 14] 45 @pc restore 174 1122 p save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 23 r save [<03E3F00E1B800C07801C07801C03801C03801C03801C03801C03801C03801C03801C03801C0380 1C03801C03801C03801C0380FC1F80> 20 18 -1 0 23] 117 @pc restore 23 r save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 18 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 42 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [<3C0000660000F30000F10000F0800000800000800000400000400000E00000E00000E00001D000 01D00003D8000388000388000704000704000704000E02000E02001C01001C01003C0380FF07E0> 19 26 -1 8 22] 121 @pc restore 41 r save [<10F8001906001E03001C01801C01C01C00C01C00E01C00E01C00E01C00E01C00E01C00E01C00C0 1C01C01C01801E03001D86001C7C001C00001C00001C00001C00001C00001C00001C00001C0000 1C00001C0000FC0000> 19 29 -1 0 23] 98 @pc restore 23 r save [<3C0000660000F30000F10000F0800000800000800000400000400000E00000E00000E00001D000 01D00003D8000388000388000704000704000704000E02000E02001C01001C01003C0380FF07E0> 19 26 -1 8 22] 121 @pc restore 39 r save [ 26 28 -2 0 31] 72 @pc restore 31 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 33 18 -1 0 36] 109 @pc restore 36 r save [ 33 18 -1 0 36] 109 @pc restore 35 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [ 9 29 -1 0 12] 105 @pc restore 11 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<07F8001C0E00300300600180C000C0C000C0C000C06001C03003801FFF801FFF001FF800180000 30000010000013C0000C30001C3800181800381C00381C00381C00381C001818001C38800C38C0 03C4C0000380> 18 28 -1 9 21] 103 @pc restore 21 r save [ 7 41 -4 10 12] 91 @pc restore 12 r save [<03E00C301818300C300E700660076007E007E007E007E007E007E006F00EF00CE818E430E3E060 0070007000300C301E181E0C0E0604030C00F0> 16 29 -2 1 21] 54 @pc restore 725 1122 p save [ 7 41 0 10 12] 93 @pc restore 30 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 42 r save [ 23 28 -2 0 28] 80 @pc restore 28 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<07F8001C0E00300300600180C000C0C000C0C000C06001C03003801FFF801FFF001FF800180000 30000010000013C0000C30001C3800181800381C00381C00381C00381C001818001C38800C38C0 03C4C0000380> 18 28 -1 9 21] 103 @pc restore 21 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 7 41 -4 10 12] 91 @pc restore 12 r save [<0F8030C0203070107818780C300C000E0006000607C70C271817300F700F6007E007E007E007E0 07E007E006E006600E700C300C18180C3003C0> 16 29 -2 1 21] 57 @pc restore 972 1122 p save [ 7 41 0 10 12] 93 @pc restore 12 r save [<60F0F060> 4 4 -4 0 12] 46 @pc restore 43 r save [ 24 28 -2 0 29] 66 @pc restore 29 r save [<03E3F00E1B800C07801C07801C03801C03801C03801C03801C03801C03801C03801C03801C0380 1C03801C03801C03801C0380FC1F80> 20 18 -1 0 23] 117 @pc restore 23 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 35 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00E000E 000E000E000E000E000E0C061E071E018C00F8> 15 29 0 0 13] 102 @pc restore 13 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 33 18 -1 0 36] 109 @pc restore 53 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 37 r save [<07F8001C0E00300300600180C000C0C000C0C000C06001C03003801FFF801FFF001FF800180000 30000010000013C0000C30001C3800181800381C00381C00381C00381C001818001C38800C38C0 03C4C0000380> 18 28 -1 9 21] 103 @pc restore 21 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [ 11 2 0 -8 14] 45 @pc restore 14 r save [ 19 26 -1 8 23] 112 @pc restore 23 r save [<03E3F00E1B800C07801C07801C03801C03801C03801C03801C03801C03801C03801C03801C0380 1C03801C03801C03801C0380FC1F80> 20 18 -1 0 23] 117 @pc restore 23 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [ 19 26 -1 8 23] 112 @pc restore 24 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 38 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00E000E 000E000E000E000E000E0C061E071E018C00F8> 15 29 0 0 13] 102 @pc restore 13 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [<008020000180300001C0700001C0700003C0680003A0E80003A0E8000720C4000711C4000711C4 000E1182000E0B82000E0B82001C0B01001C0701001C0701803C0F0380FF3FCFE0> 27 18 -1 0 30] 119 @pc restore 30 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 174 1172 p save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<00400000E00000E00000E00001D00001D00003D8000388000388000704000704000704000E0200 0E02001C01001C01003C0380FF07E0> 19 18 -1 0 22] 118 @pc restore 22 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 19 26 -1 8 23] 112 @pc restore 23 r save [ 33 18 -1 0 36] 109 @pc restore 35 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 29 r save [ 19 26 -1 8 23] 112 @pc restore 24 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 30 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00E000E 000E000E000E000E000E0C061E071E018C00F8> 15 29 0 0 13] 102 @pc restore 28 r save [<00400000E00000E00000E00001D00001D00003D8000388000388000704000704000704000E0200 0E02001C01001C01003C0380FF07E0> 19 18 -1 0 22] 118 @pc restore 22 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<008020000180300001C0700001C0700003C0680003A0E80003A0E8000720C4000711C4000711C4 000E1182000E0B82000E0B82001C0B01001C0701001C0701803C0F0380FF3FCFE0> 27 18 -1 0 30] 119 @pc restore 30 r save [<804020201010101070F0F060> 4 12 -4 8 12] 44 @pc restore 28 r save [<008020000180300001C0700001C0700003C0680003A0E80003A0E8000720C4000711C4000711C4 000E1182000E0B82000E0B82001C0B01001C0701001C0701803C0F0380FF3FCFE0> 27 18 -1 0 30] 119 @pc restore 30 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 32 r save [ 19 26 -1 8 23] 112 @pc restore 23 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 19 26 -1 8 23] 112 @pc restore 24 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 40 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 34 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 23 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<7F87FC000E01C0000E01C0000E01C0000E01C0000E01C0000E01C0000E01C0000E01C0000E01C0 000E01C0000E01C0000E01C0000E01C0000E01C0000E01C0000E01C000FFFFFC000E01C0000E01 C0000E01C0000E01C0000E01C0000E01C0000E03C1800703C3C00303E3C001C1B180007E1F00> 26 29 0 0 24] 11 @pc restore 24 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 31 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00E000E 000E000E000E000E000E0C061E071E018C00F8> 15 29 0 0 13] 102 @pc restore 13 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 18 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 14 18 -1 0 18] 122 @pc restore 18 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 38 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00E000E 000E000E000E000E000E0C061E071E018C00F8> 15 29 0 0 13] 102 @pc restore 13 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [ 33 18 -1 0 36] 109 @pc restore 36 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<60F0F060> 4 4 -4 0 12] 46 @pc restore 34 r save [ 12 28 -1 0 15] 73 @pc restore 15 r save [ 20 18 -1 0 23] 110 @pc restore 38 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 23 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 23 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 174 1222 p save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 31 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 30 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00E000E 000E000E000E000E000E0C061E071E018C00F8> 15 29 0 0 13] 102 @pc restore 13 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 18 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 14 18 -1 0 18] 122 @pc restore 18 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 33 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00E000E 000E000E000E000E000E0C061E071E018C00F8> 15 29 0 0 13] 102 @pc restore 13 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [ 33 18 -1 0 36] 109 @pc restore 36 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 26 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 34 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 33 18 -1 0 36] 109 @pc restore 36 r save [ 19 26 -1 8 23] 112 @pc restore 23 r save [ 9 29 -1 0 12] 108 @pc restore 11 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 33 18 -1 0 36] 109 @pc restore 35 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 11 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 32 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<804020201010101070F0F060> 4 12 -4 8 12] 44 @pc restore 23 r save [<008020000180300001C0700001C0700003C0680003A0E80003A0E8000720C4000711C4000711C4 000E1182000E0B82000E0B82001C0B01001C0701001C0701803C0F0380FF3FCFE0> 27 18 -1 0 30] 119 @pc restore 30 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 28 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<008020000180300001C0700001C0700003C0680003A0E80003A0E8000720C4000711C4000711C4 000E1182000E0B82000E0B82001C0B01001C0701001C0701803C0F0380FF3FCFE0> 27 18 -1 0 30] 119 @pc restore 40 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 30 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 19 26 -1 8 23] 112 @pc restore 23 r save [ 19 26 -1 8 23] 112 @pc restore 23 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 18 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 26 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00E000E 000E000E000E000E000E0C061E071E018C00F8> 15 29 0 0 13] 102 @pc restore 23 r save [<001F800000E060800180118007000B800E0007801C0007801C0007803800078078000780780007 8070000780F0000F80F000FFF0F0000000F0000000F0000000F0000000F0000000F00000007000 00807800008078000080380001801C0001801C0003800E000380070007800180198000E0618000 1F8080> 28 30 -2 1 33] 71 @pc restore 33 r save [<00000F0000001F8000003FC000003FC0000038E00000306000006020003FE02000F0E02003A078 0007205C000E208E001C1107003C0E078038000380780003C0780003C0700001C0F00001E0F000 01E0F00001E0F00001E0F00001E0F00001E0F00001E0F00001E0700001C0780003C0780003C038 0003803C0007801C0007000E000E0007001C000380380000E0E000003F8000> 27 37 -2 8 32] 81 @pc restore 32 r save [<000007C0FFF01C200F003C200F0038100F0078100F0078100F0078000F0078000F0078000F0078 000F0078000F0078000F00F0000F00E0000F03C0000FFF00000F01E0000F0078000F003C000F00 1C000F001E000F001E000F001E000F001E000F001C000F003C000F0078000F01E000FFFF0000> 28 29 -2 1 31] 82 @pc restore 174 1272 p save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00E000E 000E000E000E000E000E0C061E071E018C00F8> 15 29 0 0 13] 102 @pc restore 13 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 18 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 14 18 -1 0 18] 122 @pc restore 18 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 36 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 20 18 -1 0 23] 110 @pc restore 37 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [<00400000E00000E00000E00001D00001D00003D8000388000388000704000704000704000E0200 0E02001C01001C01003C0380FF07E0> 19 18 -1 0 22] 118 @pc restore 22 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<07F8001C0E00300300600180C000C0C000C0C000C06001C03003801FFF801FFF001FF800180000 30000010000013C0000C30001C3800181800381C00381C00381C00381C001818001C38800C38C0 03C4C0000380> 18 28 -1 9 21] 103 @pc restore 33 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 33 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 30 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<003FE000070000070000070000070000070000070000070007C7000C3700180F00300F00700700 600700E00700E00700E00700E00700E00700E00700700700700700300F00180B000C330003C100> 19 26 -2 8 22] 113 @pc restore 22 r save [<03E3F00E1B800C07801C07801C03801C03801C03801C03801C03801C03801C03801C03801C0380 1C03801C03801C03801C0380FC1F80> 20 18 -1 0 23] 117 @pc restore 23 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [<3C0000660000F30000F10000F0800000800000800000400000400000E00000E00000E00001D000 01D00003D8000388000388000704000704000704000E02000E02001C01001C01003C0380FF07E0> 19 26 -1 8 22] 121 @pc restore 34 r save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 18 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 29 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 30 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<003FE000070000070000070000070000070000070000070007C7000C3700180F00300F00700700 600700E00700E00700E00700E00700E00700E00700700700700700300F00180B000C330003C100> 19 26 -2 8 22] 113 @pc restore 22 r save [<03E3F00E1B800C07801C07801C03801C03801C03801C03801C03801C03801C03801C03801C0380 1C03801C03801C03801C0380FC1F80> 20 18 -1 0 23] 117 @pc restore 23 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 33 r save [ 19 26 -1 8 23] 112 @pc restore 23 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<10F8001906001E03001C01801C01C01C00C01C00E01C00E01C00E01C00E01C00E01C00E01C00C0 1C01C01C01801E03001D86001C7C001C00001C00001C00001C00001C00001C00001C00001C0000 1C00001C0000FC0000> 19 29 -1 0 23] 98 @pc restore 23 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 33 18 -1 0 36] 109 @pc restore 36 r save [<804020201010101070F0F060> 4 12 -4 8 12] 44 @pc restore 25 r save [<07F8001C0E00300300600180C000C0C000C0C000C06001C03003801FFF801FFF001FF800180000 30000010000013C0000C30001C3800181800381C00381C00381C00381C001818001C38800C38C0 03C4C0000380> 18 28 -1 9 21] 103 @pc restore 21 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 14 18 -1 0 18] 122 @pc restore 18 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 174 1322 p save [ 9 29 -1 0 12] 108 @pc restore 12 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 29 r save [ 33 18 -1 0 36] 109 @pc restore 36 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 22 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [<60F0F060> 4 4 -4 0 12] 46 @pc restore 28 r save [ 12 28 -1 0 15] 73 @pc restore 15 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 30 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 29 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 37 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 34 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<008020000180300001C0700001C0700003C0680003A0E80003A0E8000720C4000711C4000711C4 000E1182000E0B82000E0B82001C0B01001C0701001C0701803C0F0380FF3FCFE0> 27 18 -1 0 30] 119 @pc restore 42 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 33 r save [ 19 26 -1 8 23] 112 @pc restore 24 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<10F8001906001E03001C01801C01C01C00C01C00E01C00E01C00E01C00E01C00E01C00E01C00C0 1C01C01C01801E03001D86001C7C001C00001C00001C00001C00001C00001C00001C00001C0000 1C00001C0000FC0000> 19 29 -1 0 23] 98 @pc restore 23 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 32 r save [<03E3F00E1B800C07801C07801C03801C03801C03801C03801C03801C03801C03801C03801C0380 1C03801C03801C03801C0380FC1F80> 20 18 -1 0 23] 117 @pc restore 23 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<07F8001C0E00300300600180C000C0C000C0C000C06001C03003801FFF801FFF001FF800180000 30000010000013C0000C30001C3800181800381C00381C00381C00381C001818001C38800C38C0 03C4C0000380> 18 28 -1 9 21] 103 @pc restore 21 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 31 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00E000E 000E000E000E000E000E0C061E071E018C00F8> 15 29 0 0 13] 102 @pc restore 26 r save [ 21 28 -2 0 26] 76 @pc restore 26 r save [ 28 29 -1 0 31] 65 @pc restore 31 r save [ 23 28 -2 0 28] 80 @pc restore 26 r save [ 28 29 -1 0 31] 65 @pc restore 31 r save [<001FC00000E0300001800800070004000E0002001C0001001C0001003800008078000080780000 8070000080F0000000F0000000F0000000F0000000F0000000F0000000F0000000F00000007000 00807800008078000080380001801C0001801C0003800E000380070007800180198000E0618000 1F8080> 25 30 -2 1 30] 67 @pc restore 30 r save [ 28 28 -2 0 32] 75 @pc restore 44 r save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 18 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 22 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 31 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00E000E 000E000E000E000E000E0C061E071E018C00F8> 15 29 0 0 13] 102 @pc restore 13 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 29 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [<00400000E00000E00000E00001D00001D00003D8000388000388000704000704000704000E0200 0E02001C01001C01003C0380FF07E0> 19 18 -1 0 22] 118 @pc restore 22 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<07F8001C0E00300300600180C000C0C000C0C000C06001C03003801FFF801FFF001FF800180000 30000010000013C0000C30001C3800181800381C00381C00381C00381C001818001C38800C38C0 03C4C0000380> 18 28 -1 9 21] 103 @pc restore 34 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 174 1371 p save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 18 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 29 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00E000E 000E000E000E000E000E0C061E071E018C00F8> 15 29 0 0 13] 102 @pc restore 25 r save [<07F8001C0E00300300600180C000C0C000C0C000C06001C03003801FFF801FFF001FF800180000 30000010000013C0000C30001C3800181800381C00381C00381C00381C001818001C38800C38C0 03C4C0000380> 18 28 -1 9 21] 103 @pc restore 21 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 14 18 -1 0 18] 122 @pc restore 18 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 36 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 29 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<003FE000070000070000070000070000070000070000070007C7000C3700180F00300F00700700 600700E00700E00700E00700E00700E00700E00700700700700700300F00180B000C330003C100> 19 26 -2 8 22] 113 @pc restore 22 r save [<03E3F00E1B800C07801C07801C03801C03801C03801C03801C03801C03801C03801C03801C0380 1C03801C03801C03801C0380FC1F80> 20 18 -1 0 23] 117 @pc restore 23 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 31 r save [ 19 26 -1 8 23] 112 @pc restore 23 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [<10F8001906001E03001C01801C01C01C00C01C00E01C00E01C00E01C00E01C00E01C00E01C00C0 1C01C01C01801E03001D86001C7C001C00001C00001C00001C00001C00001C00001C00001C0000 1C00001C0000FC0000> 19 29 -1 0 23] 98 @pc restore 23 r save [ 9 29 -1 0 12] 108 @pc restore 12 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 33 18 -1 0 36] 109 @pc restore 36 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 28 r save [<008020000180300001C0700001C0700003C0680003A0E80003A0E8000720C4000711C4000711C4 000E1182000E0B82000E0B82001C0B01001C0701001C0701803C0F0380FF3FCFE0> 27 18 -1 0 30] 119 @pc restore 30 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 33 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 31 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00E000E 000E000E000E000E000E0C061E071E018C00F8> 15 29 0 0 13] 102 @pc restore 13 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 33 18 -1 0 36] 109 @pc restore 47 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 19 26 -1 8 23] 112 @pc restore 23 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 33 18 -1 0 36] 109 @pc restore 36 r save [ 9 29 -1 0 12] 105 @pc restore 11 r save [ 14 18 -1 0 18] 122 @pc restore 18 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 34 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<07C7E00C3700180F00300700700700600700E00700E00700E00700E00700E00700E00700600700 700700300700180F000C170003E700000700000700000700000700000700000700000700000700 000700000700003F00> 19 29 -2 0 23] 100 @pc restore 35 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<03C00E200C101C101C101C101C101C101C001C001C001C001C001C001C001C001C00FFE03C001C 000C000C000400040004000400> 12 26 -1 0 16] 116 @pc restore 16 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 18 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 30 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 174 1421 p save [ 20 29 -1 0 23] 104 @pc restore 23 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [<07F8001C0E00300300600180C000C0C000C0C000C06001C03003801FFF801FFF001FF800180000 30000010000013C0000C30001C3800181800381C00381C00381C00381C001818001C38800C38C0 03C4C0000380> 18 28 -1 9 21] 103 @pc restore 21 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [ 11 2 0 -8 14] 45 @pc restore 14 r save [ 19 26 -1 8 23] 112 @pc restore 24 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [<7FE00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00E000E 000E000E000E000E000E0C061E071E018C00F8> 15 29 0 0 13] 102 @pc restore 13 r save [<03F0000E1C00180600300300700380600180E001C0E001C0E001C0E001C0E001C0E001C0600180 7003803003001806000E1C0003F000> 18 18 -1 0 21] 111 @pc restore 21 r save [ 13 18 -1 0 16] 114 @pc restore 16 r save [ 33 18 -1 0 36] 109 @pc restore 36 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 18 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 31 r save [ 33 18 -1 0 36] 109 @pc restore 36 r save [<1F8700304E80603C40E01C40E01C40E01C40601C00701C00381C000F1C0001FC00001C00001C00 301C00781C007838003070001FC000> 18 18 -2 0 21] 97 @pc restore 21 r save [<07C00C301808300470046000E000E000E000E000E000E00060007030307818780C3007E0> 14 18 -2 0 18] 99 @pc restore 17 r save [ 20 29 -1 0 23] 104 @pc restore 23 r save [ 9 29 -1 0 12] 105 @pc restore 12 r save [ 20 18 -1 0 23] 110 @pc restore 23 r save [<03E00C181804300270026000E000E000E000E000FFFEE0066006700E300C18180C3003E0> 15 18 -1 0 18] 101 @pc restore 18 r save [<8FC0D060E010C018C0188018803800F80FF03FE07F80F800E010C010C010403030701F90> 13 18 -1 0 16] 115 @pc restore 16 r save [<60F0F060> 4 4 -4 0 12] 46 @pc restore cmbx10.432 @sf 60 1573 p save [<7FFFFE7FFFFE7FFFFE00FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE00 00FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE00 00FE0000FE0000FE0000FE0000FE0000FE00F8FE00FFFE00FFFE0007FE00007E00001E00000E00> 23 39 -5 0 34] 49 @pc restore 163 1573 p save [ 22 41 -2 0 26] 73 @pc restore 26 r m (n) -1 (tro) 2 (d) ks save [<003FC3FF8001FFF3FF8003F03BFF8007E00FF80007E007F8000FE007F8000FE003F8000FE003F8 000FE003F8000FE003F8000FE003F8000FE003F8000FE003F8000FE003F8000FE003F8000FE003 F8000FE003F8000FE003F8000FE003F8000FE003F8000FE003F8000FE003F8000FE003F8000FE0 03F800FFE03FF800FFE03FF800FFE03FF800> 33 27 -3 0 38] 117 @pc restore 38 r m (ct) s save [ 15 43 -3 0 20] 105 @pc restore 20 r m (on) s cmr10.329 @sf 60 1683 p m (QR) 16 (factorization) 15 (of) 15 (an) ks cmmi10.329 @sf 15 r m (n) s cmr10.329 @sf 15 r m (b) 0 (y) ks cmmi10.329 @sf 14 r m (m) s cmr10.329 @sf 15 r m (matrix) s cmmi10.329 @sf 15 r m (A) s cmr10.329 @sf 16 r m (assumes) 15 (the) 15 (form) ks cmmi10.329 @sf 877 1785 p m (A) s cmr10.329 @sf 13 r m (=) s cmmi10.329 @sf 13 r m (QR) s cmr10.329 @sf 60 1887 p m (where) s cmmi10.329 @sf 17 r m (Q) s cmr10.329 @sf 17 r m (is) 18 (an) ks cmmi10.329 @sf 17 r m (n) s cmr10.329 @sf 17 r m (b) 0 (y) ks cmmi10.329 @sf 16 r m (n) s cmr10.329 @sf 17 r m (orthogonal) 16 (matrix,) ks cmmi10.329 @sf 17 r m (R) s cmr10.329 @sf 16 r m (=) s cmmi10.329 @sf 16 r m (Q) s cmr8.300 @sf 1042 1872 p m (T) s cmmi10.329 @sf 1069 1887 p m (A) s cmr10.329 @sf 17 r m (is) 18 (zero) 16 (b) 1 (elo) 0 (w) 17 (its) 17 (diagonal.) 26 (If) ks cmmi10.329 @sf 17 r m (n) s cmsy10.329 @sf 16 r save [ 26 36 -4 7 35] 21 @pc restore cmmi10.329 @sf 51 r m (m) s cmr10.329 @sf m (,) s 60 1943 p m (then) s cmmi10.329 @sf 16 r m (Q) s cmr8.300 @sf 200 1928 p m (T) s cmmi10.329 @sf 227 1943 p m (A) s cmr10.329 @sf 15 r m (can) 16 (b) 1 (e) 15 (written) 16 (in) 16 (the) 15 (form) ks cmmi10.329 @sf 818 2076 p m (Q) s cmr8.300 @sf 854 2058 p m (T) s cmmi10.329 @sf 882 2076 p m (A) s cmr10.329 @sf 13 r m (=) s cmex10.300 @sf 977 2004 p save [ 12 124 -11 122 24] 34 @pc restore cmmi10.329 @sf 1022 2049 p m (R) s cmr10.329 @sf 1028 2104 p m (0) s cmex10.300 @sf 1077 2004 p save [ 12 124 0 122 24] 35 @pc restore cmr10.329 @sf 60 2208 p m (where) s cmmi10.329 @sf 16 r m (R) s cmr10.329 @sf 15 r m (is) 16 (an) ks cmmi10.329 @sf 16 r m (n) s cmr10.329 @sf 16 r m (b) 0 (y) ks cmmi10.329 @sf 14 r m (n) s cmr10.329 @sf 16 r m (upp) 1 (er) 17 (triangular.) 21 (If) ks cmmi10.329 @sf 16 r m (n) s 14 r save [<000001C00000078000001E00000078000001E00000078000000E00000038000000F0000003C000 000F0000003C000000F0000000F00000003C0000000F00000003C0000000F0000000380000000E 0000000780000001E0000000780000001E0000000780000001C0> 26 26 -4 2 35] 60 @pc restore 48 r m (m) s cmr10.329 @sf m (,) 16 (then) 16 (the) 15 (QR) 17 (factorization) 15 (of) ks cmmi10.329 @sf 15 r m (A) s cmr10.329 @sf 16 r m (assumes) s 60 2264 p m (the) 15 (form) ks cmmi10.329 @sf 787 2321 p m (Q) s cmr8.300 @sf 823 2303 p m (T) s cmmi10.329 @sf 851 2321 p m (A) s cmr10.329 @sf 12 r m (=) s cmex10.300 @sf 945 2274 p m (h) s cmmi10.329 @sf 986 2321 p m (R) s 1062 2321 p m (S) s cmex10.300 @sf 1113 2274 p m (i) s cmr10.329 @sf 60 2409 p m (where) s cmmi10.329 @sf 13 r m (R) s cmr10.329 @sf 12 r m (is) 14 (an) ks cmmi10.329 @sf 12 r m (n) s cmr10.329 @sf 13 r m (b) 0 (y) ks cmmi10.329 @sf 12 r m (n) s cmr10.329 @sf 13 r m (upp) 1 (er) 13 (triangular) 13 (matrix.) 19 (Ho) 0 (w) -1 (ev) -1 (er,) 11 (in) 13 (practical) 14 (applications,) 14 (it) 13 (is) 13 (more) ks 60 2466 p m (con) 0 (v) 0 (enien) 0 (t) 13 (to) 14 (represen) 0 (t) 15 (the) 15 (factorization) 15 (in) 16 (this) 15 (case) 16 (as) ks cmmi10.329 @sf 795 2573 p m (A) s cmr10.329 @sf 12 r m (=) s cmex10.300 @sf 889 2526 p m (h) s cmr10.329 @sf 930 2573 p m (0) s cmmi10.329 @sf 994 2573 p m (R) s cmex10.300 @sf 1050 2526 p m (i) s cmmi10.329 @sf 1077 2573 p m (Q;) s 60 2630 p 720 2 ru 111 2658 p save [<0C000C008C40EDC07F800C007F80EDC08C400C000C00> 10 11 -3 -1 16] 3 @pc restore cmr9.300 @sf 129 2673 p save [<03FFE000001C0000001C0000001C0000001C0000001C0000001C0000001C0000001C0000001C00 00001C0000001C0000001C0000001C0000001C0000001C0000001C0000001C0000801C0080801C 0080801C0080C01C0180401C0100401C0100701C07007FFFFF00> 25 26 -1 0 28] 84 @pc restore 28 r save [ 18 26 -1 0 21] 104 @pc restore 21 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 29 r save [<010040000180C0000380E0000380E00003C1E0000741D000074190000F2398000E2388000E2308 001E170C001C1704001C160400380E06003C0E0700FF3F9F80> 25 16 -1 0 28] 119 @pc restore 28 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [ 18 26 -1 0 20] 107 @pc restore 32 r save [<010040000180C0000380E0000380E00003C1E0000741D000074190000F2398000E2388000E2308 001E170C001C1704001C160400380E06003C0E0700FF3F9F80> 25 16 -1 0 28] 119 @pc restore 28 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 27 r save [<8F80F040C020C0308030807000F01FE03FC07F00F000C020C020402060E01F20> 12 16 -1 0 15] 115 @pc restore 15 r save [<07CFC00C2E001C1E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E00 1C0E001C0E00FC7E00> 18 16 -1 0 21] 117 @pc restore 21 r save [ 18 23 -1 7 21] 112 @pc restore 21 r save [ 18 23 -1 7 21] 112 @pc restore 22 r save [<07E01C38381C700E6006E007E007E007E007E007E0076006700E300C1C3807E0> 16 16 -1 0 19] 111 @pc restore 19 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 15 r save [<07E00C18380830046000E000E000E000E000FFFCE00C600C701830181C3007C0> 14 16 -1 0 17] 101 @pc restore 17 r save [<07CFC01C2E00381E00700E00600E00E00E00E00E00E00E00E00E00E00E00E00E00700E00300E00 380E000C3E0003CE00000E00000E00000E00000E00000E00000E00000E00000E00000E00007E00> 18 26 -1 0 21] 100 @pc restore 35 r save [ 9 26 0 0 10] 105 @pc restore 10 r save [ 18 16 -1 0 21] 110 @pc restore 35 r save [ 18 23 -1 7 21] 112 @pc restore 21 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 28 r save [<10F0001B0C001E07001C03001C03801C01C01C01C01C01C01C01C01C01C01C01C01C01801C0380 1E07001F0E001CF8001C00001C00001C00001C00001C00001C00001C00001C00001C0000FC0000> 18 26 -1 0 21] 98 @pc restore 21 r save [<780000E40000E20000E1000001000001000000800000800001C00001C00001C00003A00003A000 0790000710000710000E08000E08001E0C001C04001C04003C0600FF1F80> 17 23 -1 7 20] 121 @pc restore 33 r save [ 24 26 -2 0 29] 78 @pc restore 29 r save [<87E0D818E004C006C00280038003800300030007000E003E07FC1FF83FE07E007000E000C002C0 02C002C0066006200E18360FC2> 16 26 -2 0 21] 83 @pc restore 21 r save [ 20 26 -2 0 25] 70 @pc restore 37 r save [<07E0381C6006C003C003C003C003600F1FFE3FFC3FF07000600020002FC0186030307038703870 387038303018730FCE> 16 24 -1 8 19] 103 @pc restore 19 r save [ 12 16 -1 0 15] 114 @pc restore 15 r save [<1E3C71FBE0F1E071E071E070707030701C7007F000700070207070E070C03F80> 16 16 -2 0 19] 97 @pc restore 19 r save [ 18 16 -1 0 21] 110 @pc restore 21 r save [<03800E401C201C201C201C201C201C001C001C001C001C001C001C001C00FFC03C001C000C000C 00040004000400> 11 23 -1 0 15] 116 @pc restore 28 r save [ 26 26 -1 0 29] 65 @pc restore 29 r save [<87E0D818E004C006C00280038003800300030007000E003E07FC1FF83FE07E007000E000C002C0 02C002C0066006200E18360FC2> 16 26 -2 0 21] 83 @pc restore 21 r save [<003F0001C0C00300300E00081C00081C0004380004780002700002700002F00000F00000F00000 F00000F00000F000007000027000027800023800061C00061C000E0E001E03002E01C0C6003F02> 23 26 -2 0 28] 67 @pc restore 28 r save [ 10 2 0 -7 13] 45 @pc restore 13 r save [ 18 16 -1 0 20] 120 @pc restore 20 r save [ 18 16 -1 0 20] 120 @pc restore 20 r save [ 18 16 -1 0 20] 120 @pc restore 20 r save [ 18 16 -1 0 20] 120 @pc restore cmr10.329 @sf 949 2828 p m (1) s @eop @end .